Nos. 96-1193, 96-1286, 96-1458, 982, 947, 1116.United States Court of Appeals, Second Circuit.Argued: January 22, 1997.
Decided: March 25, 1997.
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Robert E. Rice, Assistant United States Attorney, New York City (Mary Jo White, United States Attorney for the Southern District of New York, Rose A. Gill, Marian W. Payson, Assistant United States Attorneys, New York City, on the brief), for Appellee.
Steven Jay Harfenist, Bayside, N Y (Friedman Harfenist, Bayside, NY, on the brief), for Defendant-Appellant Robert Maher.
David I. Schoen, New York City, for Defendant-Appellant Andrew Giordano.
Appeals from judgments of the United States District Court for the Southern District of New York, Louis L. Stanton, Judge, convicting defendants of money laundering offenses, 18 U.S.C. Section(s) 371 and 1956(a)(1)(B)(i) and (f), and requiring them to forfeit $7,000,293.15 under 18 U.S.C. §(s) 982(a)(1) and (b)(1)(A). Affirmed.
Before: KEARSE and JACOBS, Circuit Judges, and GLEESON, District Judge .
KEARSE, Circuit Judge:
 Defendants Robert Maher, Peter Mancusi, and Andrew Giordano appeal from judgments of conviction entered in the United States District Court for the Southern District of New York following their pleas of guilty before Louis L. Stanton, Judge, to charges of conspiring to launder money in violation of 18 U.S.C. Section(s) 371 (1994), and money laundering, in violation of 18 U.S.C. §(s) 1956(a)(1)(B)(i) and (f) (1994) and 18 U.S.C. Section(s) 2 (1994). Maher was sentenced principally to 135 months’ imprisonment, to be followed by three years of supervised release; Mancusi was sentenced principally to 108 months’ imprisonment, to be followed by two years of supervised release; Giordano was sentenced principally to 151 months’ imprisonment, to be followed by three years of supervised release. In addition, pursuant to 18 U.S.C. §(s) 982(a)(1) and (b)(1)(A) (1994), each defendant was ordered to forfeit his respective interest in $7,000,293.15 in laundered money, the proceeds of narcotics trafficking. On appeal, defendants contend chiefly that the district court erred in accepting their guilty pleas or in refusing to allow them to withdraw those pleas. Mancusi and Giordano also challenge their sentences. Finding no merit in defendants’ challenges to their pleas, and finding that the sentencing challenges have been waived, we affirm the judgments.
 I. BACKGROUND
 The present proceedings arise out of a 59-count indictment that charged each defendant
with, inter alia, laundering, on 14 specified occasions, a total of approximately $7,000,293.15 derived from narcotics trafficking, knowing that the money represented the proceeds of some form of unlawful activity and intending to conceal the source, location, or ownership of the money, in violation of 18 U.S.C. §(s) 1956(a)(1)(B)(i) and (f) and 18 U.S.C. §(s) 2 (count 2); and with conspiring to do so, in violation of 18 U.S.C. §(s) 371 (count 1); and seeking forfeiture of the $7,000,293.15 (count 59). The indictment also alleged numerous counts of other money laundering offenses, as well as failure to file currency reports, and interstate and foreign travel in aid of racketeering activity.
 The government contended that the laundered money was the proceeds of narcotics trafficking conducted by an international conspiracy that included Thongchai Sanguandikul, a resident of Thailand, and Albert Castagnola, a resident of Pennsylvania. A jury trial began on October 23, 1995, and continued for two weeks. The 25 witnesses called by the government included private citizens from the United States and Asia, law enforcement agents, and Castagnola. The proof at trial, taken in the light most favorable to the government, showed the following.
 A. The Trial Evidence
 In the late 1980s, Sanguandikul was a foreign supplier of large quantities of heroin imported into the United States and Mexico. Raphael Santana, a buyer, arranged for payment by having Castagnola transfer money by wire to a Hong Kong bank account; the money was then transferred to the Shun Lee Company in Bangkok, Thailand, from which it was accessible to Sanguandikul. In 1989, however, Castagnola was arrested; he pleaded guilty to conspiring to import heroin and to money laundering, and he agreed to cooperate with the government. After Castagnola was arrested, Sanguandikul traveled to New York City, where defendants were located, and defendants soon began to deposit hundreds of thousands of dollars into Hong Kong bank accounts controlled by Sanguandikul. The evidence as to defendants’ activities, which included testimony from employees of banks and other companies whose services were used, testimony from customs agents and other law enforcement officials, and records seized from offices shared by Giordano and Maher and from their respective homes, included the following.
 First, Maher began delivering hundreds of thousands of dollars in cash to Giordano. Giordano in turn delivered hundreds of thousands of dollars to Mancusi. Giordano and Mancusi, along with their sons and Giordano’s employees, converted large sums of cash from small-denomination bills to $50 and $100 bills at New York City area banks. Mancusi, charging part of his travel expenses to an account maintained by Giordano, proceeded to make 14 trips to Hong Kong, carrying cash, mostly in $100 bills, which he deposited there in accounts controlled by Sanguandikul. The amounts ranged from $179,673 to $1,047,324 and totaled more than $7 million. To demonstrate the furtive nature of these actions, the government showed that, although Mancusi in 1985 had filed a currency report when he traveled to Liberia carrying $44,750, on none of his Hong Kong trips did he file the required reports that he was transporting more than $10,000 out of the United States.
 Mancusi’s deposits in Hong Kong were closely monitored by Sanguandikul, who would then arrange for their transfer to the Shun Lee Company. Law enforcement agents found copies of telefaxes sent from offices shared by Giordano and Maher and from Giordano’s home to Sanguandikul, who, according to Castagnola’s testimony, was also known as “Joe.” In the Giordano-Maher offices the agents also found telephone and pager numbers in Bangkok for “Mr. Joe”; and there was evidence that Maher had sent packages, bearing a false return address, to “Joe” in Bangkok. Maher’s packages were sent to a Bangkok hair salon at which Sanguandikul’s wife was a hairdresser; in a document filed with the Thai government, Sanguandikul had given the salon’s address as his own.
 Sanguandikul was eventually arrested in Hong Kong and extradited to the United
States, where he was tried for and convicted of conspiracy to import heroin.
 B. The Pleas of Guilty and the Attempts To Withdraw Those Pleas
 On November 6, 1995, after two weeks of trial at which the government had presented evidence, including that summarized above, through the testimony of 25 of its 26 scheduled witnesses, defendants’ attorneys approached the government about changing defendants’ pleas to guilty. After a recess granted by the court, the defendants signed agreements on that day agreeing, inter alia, to plead guilty to counts 1 (conspiracy), 2 (money laundering), and 59 (forfeiture); in return, the government agreed, inter alia, to move to dismiss the remaining counts. As discussed in Part II.E. below, in their respective plea agreements defendants entered into various stipulations as to sentencing. As discussed in Parts II.A. and B. below, the district court conducted individual plea inquiries pursuant to Rule 11 of the Federal Rules of Criminal Procedure and thereafter accepted the guilty pleas of all three defendants.
 On April 15, 1996, Mancusi, who was scheduled to be sentenced on April 24, moved to withdraw his plea of guilty. Represented by new counsel, he argued principally that the evidence the government had presented at trial was insufficient to establish his guilt and that the assistance of his former counsel in advising him as to the strength of the government’s case had been ineffective. The district court denied the motion, stating, inter alia, that [a] rational juror would have been hard pressed to avoid finding that the money Mancusi carried to Hong Kong was proceeds from narcotics trafficking. The exchange of small denomination bills (which are used in street-level narcotics transactions) for larger ones, the physical transportation of the money to Hong Kong rather than a more easily traced method of transfer, Giordano and Maher’s contact with Sanguandikul, Mancusi’s repeated receipt of large cash amounts from Giordano, and his failure to file currency reports all but compel the inference that the money was proceeds of narcotics trafficking.
 Memorandum Endorsement, dated April 23, 1996, at 2 (emphasis added). The court further concluded that the evidence itself showed that Mancusi’s counsel’s advice that the government had presented a strong case was not ineffective assistance.
 On May 22, 1996, Giordano, who was scheduled to be sentenced on June 25, similarly moved to withdraw his plea of guilty. Likewise represented by new counsel, he argued principally that he was actually innocent because in fact Mancusi had received the funds in question in Hong Kong from Korean investors for a project in Liberia. One of the supporting affidavits submitted by Giordano was an extensive affidavit from Mancusi dated May 20, 1996, describing his own and Giordano’s innocence. (Mancusi had not submitted such an affidavit in support of his motion to withdraw his own plea, and by May 20 he had been sentenced.) Giordano argued that there was no adequate factual basis for his plea, that he had not knowingly and voluntarily entered into his plea agreement because he did not understand it, and that his former counsel had rendered ineffective assistance in advising him to plead guilty. He also claimed that counsel had coerced him to plead guilty by demanding more money to continue with the trial.
 The district court denied Giordano’s motion to withdraw his plea, finding, inter alia, that most aspects of Giordano’s new contentions were contradicted by his sworn admissions during his plea allocution. Noting Giordano’s plea-hearing descriptions of his own and Mancusi’s conduct, the court characterized the new Korean-investors explanation as “highly improbable” and “fiction”; the court also found that there had been adduced at trial “ample evidence that the money was in fact proceeds of narcotics trafficking.” Memorandum and Order, dated June 21, 1996, at 6, 5, 10. The court further found that Giordano’s statements and demeanor during his plea allocution belied the new contention that he did not understand the plea agreement, and that his stated satisfaction with counsel’s assistance when he entered his plea was more credible than his belated assertions of ineffectiveness. The
court also concluded that, “[i]n light of the overwhelming evidence presented during the government’s case and the possibility that Mancusi might testify as a cooperating witness, the advice of Giordano’s counsel that he accept the benefits of a guilty plea” was not ineffective. Id. at 11. With respect to Giordano’s claim that counsel had coerced him to plead guilty, the court evaluated tape recordings that Giordano had made of telephone conversations with his former counsel; the court found that the tapes showed no sign of reluctance on counsel’s part to continue with the trial, but rather showed that the attorney-client relationship soured over fee disputes months after the guilty plea was entered. Finally, the court noted that granting the motion to withdraw the plea of guilty and requiring a new trial would be extremely prejudicial to the government. The court distinguished the present case from cases in which there is no prejudice to the government from allowing withdrawal of a plea, improvidently made, before trial. Here, the plea was not made until after the defendants and jury had sat through extensive testimony from over a score of witnesses, many transported from the Far East at considerable expense. Allowing withdrawal of the plea at this juncture would severely prejudice the government, which has displayed its case in full and would be forced substantially to repeat it.
 (Id. at 12.)
 Defendants were sentenced as indicated above, and these appeals followed.
 II. DISCUSSION
 On appeal, defendants contend principally that their pleas of guilty were invalid because the district court did not comply with Rules 11(c) and (f) of the Federal Rules of Criminal Procedure. Mancusi and Giordano also contend that the court should have granted their motions to withdraw their pleas, and they challenge their sentences. All of these contentions are meritless.
 A. The Rule 11(c) Challenges
 As discussed in greater detail in Part II.B. below, Section(s) 1956(a)(1)(B)(i) makes it unlawful for a person to conduct a financial transaction involving the proceeds of a specific type of unlawful activity listed in Section(s) 1956(c)(7) if the person knows that the property involved in the financial transaction represents the proceeds of any form of felonious activity and knows that the financial transaction is designed in whole or in part to conceal or disguise the source of those proceeds. Defendants contend that in pleading guilty to violating and conspiring to violate this section, they did not understand the nature of the charges, and thus their pleas violated Rule 11(c). The record does not support their contentions.
 Rule 11(c) provides, in pertinent part, as follows:
(c) Advice to Defendant. Before accepting a plea of guilty . . ., the court must address the defendant personally in open court and inform the defendant of, and determine that the defendant understands, the following:
(1) the nature of the charge to which the plea is offered. . . .
 Fed. R. Crim. P. 11(c)(1). This Rule, which also requires the court to inform the defendant of, inter alia, the range of penalties for the crime, the right to counsel, and the rights the defendant will forgo by pleading guilty, is designed to assist the district judge in making the constitutionally required determination that a defendant’s guilty plea is truly voluntary. See, e.g., McCarthy v. United States, 394 U.S. 459, 465 (1969). We therefore require “strict adherence to the mandates of Rule 11 . . . . [and] we examine critically even slight procedural deficiencies to ensure that the defendant’s guilty plea was a voluntary and intelligent choice, and that none of the defendant’s substantial rights ha[s] been compromised.” United States v. Parkins, 25 F.3d 114, 117 (2d Cir.), cert. denied, 115 S.Ct. 530 (1994).
 But while Rule 11 imposes strict requirements on what information the district courts must convey and determine before
they accept a plea, it does “not . . . tell them precisely how to perform this important task in the great variety of cases that . . . come before them.” United States v. Saft, 558 F.2d 1073, 1079 (2d Cir. 1977) (emphasis in original). The court may of course inform the defendant of the nature of the charges by describing the elements of the offense in the court’s own words. Or the court may provide that information by reading the indictment to the defendant where the pertinent count spells out the elements of the offense and the circumstances indicate that this will be sufficient. See generally Seiller v. United States, 544 F.2d 554, 563 (2d Cir. 1975); United States v. Saft, 558 F.2d at 1076 (reading of indictment by court clerk may be sufficient). What is essential, however, is that the court determine by some means that the defendant actually understands the nature of the charges. As the Supreme Court has stated, [t]he nature of the inquiry required by Rule 11 must necessarily vary from case to case, and, therefore, we do not establish any general guidelines other than those expressed in the Rule itself. . . . In all such inquiries, matters of reality, and not mere ritual, should be controlling.
 McCarthy v. United States, 394 U.S. at 467 n. 20 (internal quotation marks and alterations omitted). The district court is entitled to accept a defendant’s statements under oath at a plea allocution as true. See Blackledge v. Allison, 431 U.S. 63, 74 (1977). This Court, in assessing a district court’s finding that the defendant understood the nature of the charges to which he pleaded guilty, is entitled to consider the entire record. See, e.g., United States v. Parkins, 25 F.3d at 118.
 Notwithstanding the detailed requirements of Rule 11(c), Rule 11 also contains a harmless-error provision:
(h) Harmless Error. Any variance from the procedures required by this rule which does not affect substantial rights shall be disregarded.
 Fed. R. Crim. P. 11(h). Though the kinds of Rule 11 violations that can properly be considered harmless error are “fairly limited,” it is clear that one of the purposes of this provision was to permit rejection of a Rule 11(c) challenge where the record plainly shows that the defendant understood the nature of the charges despite a flawed inquiry by the court, for the advisory committee stated that harmless error could properly be found where the judge’s compliance with subdivision (c)(1) was not absolutely complete, in that some essential element of the crime was not mentioned, but the defendant’s responses clearly indicate his awareness of that element.
 Fed. R. Crim. P. 11 Advisory Committee Note (1983) (Rule 11(h)). In the present case, although the district court’s statements could have been more detailed in explaining the elements of money laundering, the record plainly reveals that each defendant understood the nature of the charges to which he was pleading guilty and that the alleged error in the court’s performance of its Rule 11(c) duties was entirely harmless. After the recess on November 6, 1995, the government and defendants submitted to the court the respective plea agreements. Each defendant also submitted his own written Petition To Enter Plea of Guilty (“Plea Petition”) which he signed in the presence of his attorneys and in open court and in which he acknowledged having certain information and answered certain questions in his own words and in his own handwriting. For example, each petition contained a form paragraph that stated
I have received a copy of the Indictment (Information) before being called upon to plead, and have read and discussed it with my attorney, and believe and feel that I understand every accusation made against me in this case.
 (Plea Petition Para(s)(8)(a).) Each petition form instructed the defendant to, inter alia, set out “in his own handwriting . . . his own statement as to each count with which he is charged,” describing “what occurred which shows that I am, in fact, guilty of each charge or charges to which I am now offering to plead `GUILTY.'” (Plea Petition Para(s) 26 n.*.) In response to this instruction, Giordano, for example, wrote that
on fourteen occassions [sic], I conspired with Codefendant [sic] to transport large sums of money. The total amount was approximately six million dollars. The money was transpoted [sic] to Hong Kong. I knew the source of money was from an illegal source.
 (Giordano Plea Petition Para(s) 26.) The pertinent handwritten portion of Maher’s plea petition stated:
From Jan. 1990 to June 1991, I agreed with others to deposit monies in banks which I knew to be from unlawful activities. I knew this conduct concealed the location and source of such money. I did this on a number of occasions.
 (Maher Plea Petition Para(s) 26.) After the court reviewed the plea agreements and petitions, there followed a hearing at which all defendants and their attorneys were present, and the district court addressed each defendant personally in turn.
 First addressing Mancusi, the court determined that he had received a copy of the indictment, that he had more than once discussed the charges in the indictment with his attorney, and that he understood the charges and needed no further time to consider them:
Q. Mr. Mancusi, have you received a copy of the indictment which is the written statement of the charges against you in this case?
A. Yes, I have.
Q. And have you fully discussed those charges and the case in general with Mr. Bress as your lawyer?
A. I have, just went through it again.
Q. Are you fully satisfied with the counsel and representation and advice that you’ve received in this case from Mr. Bress, your counsel?
A. As far as Mr. Bress'[s] advice I think it was excellent, but, and I’m starting to understand the charges for what they are.
Q. You say you’re starting to understand them?
A. Right. I understand them, your Honor.
Q. Do you want more time to discuss them with Mr. Bress?
A. No, we just went over it again, and I understand it.
(Transcript, November 6, 1995 (“Tr.”), 1146-47.)
 Stating that Mancusi was “pleading to Count One which charges you with conspiracy to launder money and to Count Two which charges you with laundering money,” the court asked, “What did you do that leads you to plead guilty to those counts?” (Tr. 1153; see also id. 1158-59 with regard to count 59.) Mancusi responded:
Your Honor, in my opinion what I did that was wrong was I transported money from the United States to Hong Kong, and there I deposited in a savings account, and from that point that savings account was used, unbeknownst to me, but for illegal profit, and that’s what occurred for myself and Mr. Giordano.
 (Tr. 1154.) In addition, although Mancusi denied that the purpose of the deposits was concealment of the ownership of the money, he indicated that the purpose was to conceal its source. For example, when the court asked, referring to Mancusi’s plea petition, whether the purpose was concealment of “the source and the ownership,” Mancusi responded, “Well, see, your Honor, that’s not entirely true” and stated that the purpose was “not to conceal any ownership.” (Tr. 1154 (emphases added).) Mancusi added that he had sufficient intelligence to be aware that the funds he carried were from an unlawful source:
All I was given was the name of the savings account of this individual, and then all of the destruction [sic] came from that savings account and where it went, but I agreed I carried the money. It totaled almost seven and a half million dollars so I wasn’t a moron. I started to realize something must be wrong with this money, but then it was too late. So actually I illegally transported funds which I felt were illegal, gained by illegal enterprise.
 (Tr. 1154-55.) The court asked further questions to confirm that Mancusi deposited the transported money into accounts that were in neither his own name nor Giordano’s (see Tr. 1163), and that although Mancusi denied
knowing that the money he transported to Hong Kong came from narcotics trafficking, he knew it was the proceeds of some unlawful activity (see id. 1162 (“THE COURT: You did know that [the money you transported came from illegal sources], didn’t you, Mr. Mancusi? DEFENDANT MANCUSI: Yes. After the third trip I assumed that was the case.”)).
 Next addressing Giordano, the court questioned him in part as follows:
Q. You are familiar with Count One that charges you with conspiracy, that is, agreeing with others to launder money, with the actual laundering of the money in Count Two, and the forfeiture claim
. . . .
What did you do that leads you to plead guilty to those counts?
. . . .
A. I with other people gave Mr. Mancusi money to transport to Hong Kong which I believed came from illegal sources, but I had no idea that was drug money, your Honor, that was being put into the drug account, but I believed it was illegal sources. But we found out in court that was a big drug account group that the money was going to.
Q. What was the purpose of having it go over to Hong Kong?
A. To be put into an account.
. . . .
DEFENDANT GIORDANO: To conceal the source of the money. . . .
Q. Was the amount involved a little over $6 million?
A. 7 million, your Honor.
 Finally, addressing Maher, the court questioned him in part as follows:
Q. Have you received a copy of the indictment in this case?
A. Yes, I have, your Honor.
Q. Have you fully discussed the charges against you in this case and the case in general with Mr. Greenfield as your lawyer?
A. Yes, your Honor.
Q. You are pleading guilty to Count One which charges you with conspiracy, that is, an unlawful agreement to money launder, and guilty to Count Two which charges you with money laundering, and to Count Fifty[-]nine which seeks forfeiture of the proceeds of money laundering.
What did you do that lead[s] you to plead guilty to those crimes?
A. From January of ’90 to June of ’91 I agreed with others to deposit money in banks which I knew to be from unlawful activities. This was done to conceal the location and source of the money.
Q. Was the amount involved about $7 million?
A. Yes, your Honor.
. . . .
Q. Did you carry out those activities that you had agreed to do?
A. Yes, your Honor.
(Tr. 1190-91.) Maher added:
A. . . . . I had no idea it was going into the hands of a drug dealer.
Q. Excuse me?
A. I had no idea it was going into the hand [sic] of a drug dealer until all this compelling evidence came out over here. I just thought they were just trying to hide the, you know, hide a transaction.
 These portions of the record reveal that each defendant acknowledged that he had read the indictment, had discussed the charges with his attorney, and knew that he was pleading guilty to counts charging money laundering and conspiracy to launder money and demanding forfeiture. Further, though each defendant denied knowing that the laundered money was the proceeds of narcotics trafficking, the record indicates that those denials reflected their efforts to avoid the three-step offense level enhancement that their plea agreements stipulated were required by Sentencing Guidelines Section(s) 2S1.1(b)(1), rather than any lack of understanding of the charges against them or any effort to claim innocence of those charges.
Despite denying knowledge of the narcotics connection, defendants repeatedly acknowledged their guilt; and each defendant, when addressed personally by the court, admitted each offense element pertaining to his own conduct, stating that he had agreed to and helped to engage in a financial transaction involving money, that he knew the money was proceeds of some unlawful activity, and that the purpose of the financial transaction was to conceal the source of that money.
 It is usually the better practice for the district court in conducting plea allocutions to detail the elements of the offenses charged in the counts to which the defendants are pleading guilty or to read those counts of the indictment to them; and it would have been preferable to do so here, where the trial had proceeded on all 59 counts and defendants were pleading guilty to only three. However, we are guided by reality rather than ritual, and we conclude that any deficiency in the court’s explanation of those three counts was without a doubt harmless, for the record as a whole reveals that each defendant plainly understood the nature of the charges against him.
 B. The Claim That There Was No Factual Basis for the Pleas
 In addition to the requirements imposed by Rule 11(c), Rule 11(f) provides as follows:
(f) Determining Accuracy of Plea. Notwithstanding the acceptance of a plea of guilty, the court should not enter a judgment upon such plea without making such inquiry as shall satisfy it that there is a factual basis for the plea.
 Fed. R. Crim. P. 11(f). Defendants contend that the factual-basis requirement was violated because the government’s evidence at trial was factually insufficient to prove them guilty. We reject this contention because defendants misperceive the nature of the factual-basis requirement, the sources to which the court may look in making its determination, and the scope of Section(s) 1956(a)(1)(B)(i). In requiring the district court to satisfy itself that there is a factual basis for the plea, Rule 11(f) does not require that the court be satisfied that a jury would return a verdict of guilty. Nor does it require the court to weigh evidence to assess whether it is even more likely than not that the defendant is guilty. Indeed, when the court considers a plea of guilty prior to trial, it often has no actual evidence to assess. Rather, Rule 11(f) requires the court to assure itself simply that the conduct to which the defendant admits is in fact an offense under the statutory provision under which he is pleading guilty:
The judge must determine “that the conduct which the defendant admits constitutes the offense charged in the indictment or information or an offense included therein to which the defendant has pleaded guilty.” Requiring this examination of the relation between the law and the acts the defendant admits having committed is designed to “protect a defendant who is in the position of pleading voluntarily with an understanding of the nature of the charge but without realizing that his conduct does not actually fall within the charge.”
 McCarthy v. United States, 394 U.S. at 467 (footnotes omitted) (quoting Fed. R. Crim. P. 11 Advisory Committee Note (1966)) (emphasis ours). In making its factual-basis determination, the court is not required to rely solely on the defendant’s own admissions. The Rule does not specify that any particular type of inquiry be made. See Santobello v. New York, 404 U.S. 257, 261 . . . (1971): “Fed.Rule Crim.Proc. 11, governing pleas in federal courts, now makes clear that the sentencing judge must develop, on the record, the factual basis for the plea, as, for example, by having the accused describe the conduct that gave rise to the charge.” An inquiry might be made of the defendant, of the attorneys for the government and the defense, of the presentence report when one is available, or by whatever means is appropriate in a specific case.
 Fed. R. Crim. P. 11 Advisory Committee Note (1974) (Rule 11(f)) (emphasis omitted). Thus, so long as the facts relied on are placed on the record at the time of the plea, “the district court, in determining whether there
was a factual basis for the plea, [i]s free to rely on any facts at its disposal — not just the admissions of the defendant.” Irizarry v. United States, 508 F.2d 960, 967 (2d Cir. 1975).
 In the present case, the arguments of Mancusi and Giordano for the proposition that there was no factual basis for their pleas are essentially challenges to the strength of the evidence that the government had produced at trial. Those challenges, which are discussed in Part II.C. below, are irrelevant to the factual-basis inquiry. Maher appears to contend that there was no factual basis for his plea because he denied knowing that the money being laundered was the proceeds of narcotics trafficking. He argues that in order to establish a violation of Section(s) 1956(a)(1)(B)(i), the government must prove, inter alia, “that the defendant knows that the transaction is designed in whole or in part to conceal or disguise the nature, the location, the source or the control of the proceeds of specified unlawful activity” (Maher brief on appeal at 20), and that “for the purposes of the `unlawful activity’ and `specified unlawful activity’ elements, the factual requirements for both charges are identical and the issue before this Court the same as to both charges” (Maher brief on appeal at 21). He contends that because in his plea allocution he stated that he did not know the laundered money was going to drug dealers, the court could not find a factual basis for his plea. We disagree.
 Even assuming that the court were required to find the requisite factual basis solely in a defendant’s allocution, a proposition that is incorrect as a matter of law, and assuming that the trial evidence summarized by the government at the plea allocution were legally insufficient to show Maher’s knowledge that the money laundered here was drug money, a proposition we need not reach, we reject Maher’s factual-basis challenge because we do not accept the premise that his knowledge of the precise nature of the unlawful activity that produced the money he laundered was an element of a Section(s) 1956(a)(1)(B)(i) offense. That premise inappropriately fragments Section(s) 1956(a)(1), reading part (B)(i) out of context and subverting the plain goal of the statute.
 The substantive provisions of 18 U.S.C. §(s) 1956 under which defendants were prosecuted read as follows:
(a)(1) Whoever, knowing that the property involved in a financial transaction represents the proceeds of some form of unlawful activity, conducts or attempts to conduct such a financial transaction which in fact involves the proceeds of specified unlawful activity —
. . . .
(B) knowing that the transaction is designed in whole or in part —
. . . .
(i) to conceal or disguise the nature, the location, the source, the ownership, or the control of the proceeds of specified unlawful activity . . . shall be sentenced to a fine of not more than $500,000 or twice the value of the property involved in the transaction, whichever is greater, or imprisonment for not more than twenty years, or both.
 18 U.S.C. §(s) 1956(a)(1)(B)(i). The term “specified unlawful activity” is defined to include narcotics offenses in violation of Title 21 of the United States Code and many other federal and state crimes. See 18 U.S.C. §(s) 1956(c)(7). Subsection (c)(1) provides that, as used in Section(s) 1956(a)(1), the term “knowing that the property involved in a financial transaction represents the proceeds of some form of unlawful activity” means that the person knew the property involved in the transaction represented proceeds from some form, though not necessarily which form, of activity that constitutes a felony under State, Federal, or foreign law, regardless of whether or not such activity is specified in paragraph (7).
 Id. Section(s) 1956(c)(1). Subsection (f) gives the district court jurisdiction over foreign acts of money laundering involving more than $10,000 if the money laundering conduct occurred partly in the United States or was performed by a United States citizen. Id. Section(s) 1956(f).
 The first paragraph of Section(s) 1956(a)(1) is plainly crafted to distinguish between the actual source of laundered money and the defendant’s knowledge as to the source of that money. The language of that paragraph requires proof that the laundered property “in fact” involved the proceeds of “specified unlawful activity,” as that term is defined in subsection (f), but it does not require proof that the defendant knew what that unlawful activity was. As to the defendant’s knowledge, the government need only prove that he “kn[e]w that the property . . . represent[ed] the proceeds of some form of unlawful activity.” Id. Section(s) 1956(a)(1) (emphasis added). This clear distinction is further confirmed by subsection (c)(1)’s definition of the “knowing . . . some form of unlawful activity” phrase to mean that there must be proof that the defendant “knew” that the property to be laundered came from “some form, though not necessarily which form,” of criminal activity, 18 U.S.C. Section(s) 1956(c)(1).
 Part (B)(i) of Section(s) 1956(a)(1) too imposes a knowledge requirement, stating that the section applies to one who “know[s] that the transaction is designed . . . to conceal or disguise the . . . source [etc.] of the proceeds of specified unlawful activity.” Although it might be argued that a person could not have such knowledge as to the purpose of the transaction without also knowing the nature of the specified unlawful activity, such an interpretation of part (B)(i) would nullify the careful wording of the first paragraph of Section(s) 1956(a)(1) which evinces the clear intent to reach a person who knows that he is dealing with the proceeds of “some” crime even if he does not know precisely which crime. We conclude that part (B)(i) must be read in the context of subsection (a)(1) as a whole, and that it does not require proof that the defendant knew which “specified unlawful activity” he was helping to conceal, but only proof that he knew that a purpose of the financial transaction was concealment of the source, ownership, etc., of the funds. In sum, we view part (B)(i) as simply adding a requirement that the defendant knew of the transaction’s obfuscatory purpose.
 This interpretation is supported by the section’s legislative history. The congressional report describing the bill that included Section(s) 1956(a)(1)(B)(i) repeatedly stated that in order to come within the section, a person “need not know” that the property involved in the transaction represents the proceeds of a specific type of unlawful activity, S. Rep. No. 99-433, at 11, 12 (1986) (“Senate Report”), and explained that the goal was to negate any possible defense of lack of knowledge as to the specific type of activity that generated the funds to be laundered:
The section requires that the property involved in a transaction must in fact be proceeds of “specified unlawful activity,” and that the participant to the transaction must intend to facilitate “specified unlawful activity” or know that the transaction is designed to conceal the proceeds of “specified unlawful activity.” However, in order to fall within the section, the participant need not know that the property involved in the transaction represents the proceeds of “specified unlawful activity.” He or she need only know that it represents the proceeds of some form of unlawful activity. This distinction is drawn in order to prevent a defendant from escaping conviction by merely alleging that he or she thought the property involved represented the proceeds of a crime not covered in the term “specified unlawful activity.” It was reported to the Committee that such a defense has been successfully raised in other countries whose statutes do not draw the distinction drawn in this section and it is the Committee’s intention to avoid that result.
. . . .
. . . . As explained above, the significance of [the phrase “knowing that the property involved in a financial transaction represents the proceeds of some form of unlawful activity” as used in section (a)(1)] is that the defendant need not know exactly what crime generated the funds involved in a transaction, only that the funds are the proceeds of some kind of crime that is a felony under Federal or State law. This will eviscerate the defense that a defendant knew the funds came from a crime, but thought the crime involved
was a crime not on the list of “specified” crimes in section (c)(7).
 Senate Report at 10-12 (emphases added). Thus, in juxtaposing the knowledge requirement imposed in the first paragraph of Section(s) 1956(a)(1), with that imposed in part (B)(i), the Report stated that Section(s) 1956(a)(1) has two “knowing” requirements. In order to prove a violation of the offense [sic], the Government must show not only that the defendant knew the property involved in a transaction was the proceeds of crime, but also that the defendant either intended to facilitate a crime or knew that the transaction was designed to conceal the proceeds of a crime.
 Senate Report at 9. The explanation that the government must prove that the defendant intended to facilitate “a” crime or knew that the transaction was designed to conceal the proceeds of “a” crime confirms that the second knowledge requirement, which is found in part (B)(i), was not intended to require proof that the defendant knew the specific crime with respect to which concealment was intended. Congress plainly did not mean part (B)(i) of Section(s) 1956(a)(1) to introduce the very knowledge requirement that, in the first paragraph of the section, it had taken such pains to exclude.
 In light of Congress’s clear intent that the reach of Section(s) 1956 be broad, this Court in United States v. Stavroulakis, 952 F.2d 686, 691-92 (2d Cir.), cert. denied, 504 U.S. 926 (1992), concluded that knowledge as to what specific crime produced the money to be laundered is not required even under a subsection that does not include the “some form” language. In Stavroulakis, we considered what mens rea elements the government was required to prove in order to establish a violation of Section(s) 1956(a)(3), which makes it unlawful “to conceal or disguise the nature, location, source, ownership, or control of property believed to be the proceeds of specified unlawful activity” “with the intent . . . to promote the carrying on of specified unlawful activity.” 18 U.S.C. §(s) 1956(a)(3) (emphases added). We considered whether a defendant could be convicted of conspiracy to engage in money laundering in violation of this provision when both he and his coconspirator believed the money was the proceeds of some form of unlawful activity, but one believed the unlawful activity was narcotics trafficking and the other believed it was gambling. We ruled that, in order to commit a money laundering offense prohibited by Section(s) 1956(a)(3), a defendant need not know precisely what specified unlawful activity produced the money, so long as he believed that the money was from some unlawful activity:
Section 1956 creates the crime of money laundering, and it takes dead aim at the attempt to launder dirty money. Why and how that money got dirty is defined in other statutes. . . . The statute . . . does not distinguish among these specified unlawful activities either in degrees of importance or levels of criminal culpability. All the specified unlawful activities are clustered, almost willy-nilly, under a single definition section of the statute. So long as the cash is represented to have come from any of these activities, a defendant is guilty of the substantive offense of money laundering.
 United States v. Stavroulakis, 952 F.2d at 691 (emphasis in original). We concluded that whatever the illegal source, if it is within the statute’s definition of specified unlawful activities, “[t]he crime is the same: money laundering; the particular underlying activity specified by Congress is a necessary, but ancillary concern.” Id. (emphasis in original). The precise nature of the unlawful source, so long as it is one that is among those listed in the statute, is “an inconsequential detail” that the defendant need not have known. Id. at 692.
 These observations apply with even greater force to Section(s) 1956(a)(1), which expressly extends the scope of the prohibition to a person who merely knows that the money to be laundered was generated by “some form” of crime. Given Section(s) 1956(a)(1)’s distinction between the requirement that a defendant “know” that the money was the proceeds of “some form” of unlawful activity, and the requirement that “in fact” it was the proceeds of a “specified” unlawful activity, we conclude that a violation of Section(s) 1956(a)(1)(B)(i) is established if the government proves (1)
that the defendant conducted a financial transaction; (2) that the transaction in fact involved the proceeds of specified unlawful activity as defined in Section(s) 1956(c)(7); (3) that the defendant knew that the property involved in the financial transaction represented the proceeds of some form of unlawful activity; and (4) that the defendant knew that the financial transaction was designed in whole or in part to conceal or disguise the source, ownership, control, etc., of those proceeds.
 In the present case, the district court properly found a factual basis for each defendant’s plea of guilty. The district court addressed each defendant as described in Part II.A. above, asking what each had done that led him to plead guilty. In each instance, the defendant stated that he had agreed with others to, and had taken steps to, have money transported to Hong Kong where it would be deposited in a bank account in a name other than one of the defendants; that he knew the money was the proceeds of some unlawful activity; and that he knew the purpose of those deposits was to hide the source of the money. These admissions alone, of course, were not sufficient to establish a factual basis for the pleas, for they did not show that in fact the laundered money was the proceeds of one of the specific unlawful activities listed in Section(s) 1956(c)(7). The basis for that last element, however, was clearly provided by the attorney for the government, who, summarizing the two weeks of testimony from the witnesses at trial, described on the record some of the evidence from which it could be inferred that Sanguandikul was a large-scale heroin dealer and that the laundered money that was placed into accounts controlled by Sanguandikul was the proceeds of drug trafficking, one of the activities specified in Section(s) 1956(c)(7). Giordano and Maher, asked by the court whether they had any effective defense against the evidence described by the government, stated that they did not (Tr. 1178, 1191); Mancusi, as part of his response to the government’s recitation and the court’s question, said, “Yes, I’m guilty. I’m not saying I’m not guilty. . . .” (id. 1161). The summarized trial evidence, together with the conduct admitted by defendants, established the requisite factual basis for their pleas of guilty.
 C. The Claims of Insufficiency of the Evidence
 Mancusi, conceding that the government was not required to prove that he knew the laundered money was proceeds of specified unlawful activity but only that he knew that it was the proceeds of some form of unlawful activity, and conceding that the government did prove the latter (Mancusi brief on appeal at 9), contends that the government did not present sufficient evidence to establish that in fact the proceeds came from narcotics trafficking. He argues, for example, that because prior to Castagnola’s arrest the drug proceeds were transferred by wire, it could be inferred that defendants’ physical transport instead of cash was related to some other enterprise. Along the same lines, Giordano argues that the evidence presented by the government at trial was insufficient “in virtually every material regard” (Giordano brief on appeal at 44), that each fact relied on by the government to incriminate him “has an entirely legitimate explanation” (id. at 3), and that “the government’s case was based on nothing but inferences” (id. at 4). He argues, for example, as does Mancusi, that the government did not produce evidence as to the identity of narcotics buyers who would have paid Thongchai Sanguandikul the $7 million that Mancusi carried to Hong Kong.
 These arguments could have been made to a jury if defendants had not pleaded guilty. Insofar as this appeal is concerned, however, they have been waived, for a defendant who pleads guilty unconditionally admits his guilt and waives his right to appeal all nonjurisdictional contentions. See, e.g., Hayle v. United States, 815 F.2d 879, 881-82 (2d Cir. 1987) (factual issues waived by plea of guilty); United States v. Selby, 476 F.2d 965, 967 (2d Cir. 1973) (per curiam); United States v. Doyle, 348 F.2d 715, 718 (2d Cir.), cert. denied, 382 U.S. 843 (1965). While such a defendant retains the right to contend that there were errors in the proceedings
that led to the acceptance of his plea of guilty, and he may argue that the district court failed to comply with Rule 11(f)’s requirement that the court be satisfied “that there is a factual basis for the plea,” the latter requirement, as discussed in Part II.B. above, does not focus on the factual sufficiency or persuasiveness of the government’s evidence but rather on the relationship between (a) the law and (b) the acts the defendant admits having committed, along with other pertinent facts culled by the court from the government’s proffer or from elsewhere. Questions that a defendant might raise as to which of competing inferences should or might be drawn, or whether there are innocent explanations for behavior that could be viewed as culpable, do not survive his plea of guilty.
 In sum, where, as here, we have concluded that the district court adequately complied with the requirements of Rule 11, or where there was error but it was harmless, we will not entertain a challenge to the sufficiency of the evidence.
 D. The Challenges to the Denial of the Plea Withdrawal Motions
 We also reject the contentions of Mancusi and Giordano that the district court erred in denying their motions to withdraw their pleas of guilty. A defendant has no automatic entitlement to have such a motion granted, for “[s]ociety has a strong interest in the finality of guilty pleas,” and allowing withdrawal of pleas not only “undermines confidence in the integrity of our judicial procedures,” but also “increases the volume of judicial work, and delays and impairs the orderly administration of justice.” United States v. Sweeney, 878 F.2d 68, 70 (2d Cir. 1989) (per curiam) (internal quotation marks and alterations omitted); see also United States v. Burnett, 671 F.2d 709, 712 (2d Cir. 1982). “The fact that a defendant has a change of heart prompted by his reevaluation of either the Government’s case against him or the penalty that might be imposed is not a sufficient reason to permit withdrawal of a plea.” United States v. Gonzalez, 970 F.2d 1095, 1100 (2d Cir. 1992); see United States v. Hughes, 325 F.2d 789, 792 (2d Cir.) (belated claim of innocence not sufficient to require granting of motion to withdraw plea), cert. denied, 377 U.S. 907 (1964).
 Where a motion to withdraw a plea of guilty is made before sentencing, the court may grant the motion pursuant to Fed. R. Crim. P. 32(e) if there are valid grounds for withdrawal and granting the motion would be fair and just, giving due regard to any prejudice the government might suffer as a result. See United States v. Figueroa, 757 F.2d 466, 475 (2d Cir.), cert. denied, 474 U.S. 840 (1985). The defendant bears the burden of showing that there are valid grounds for relief. See United States v. Rodriguez, 968 F.2d 130, 140-41 (2d Cir.), cert. denied, 506 U.S. 847
(1992); United States v. Quinones, 906 F.2d 924, 928 (2d Cir. 1990), cert. denied, 498 U.S. 1069 (1991). Only if the defendant makes such a showing will the government be required to show prejudice, and then the court must exercise its discretion in balancing these competing concerns. See United States v. Figueroa, 757 F.2d at 475-76; United States v. Saft, 558 F.2d at 1083. The district court may require an evidentiary hearing if the defendant has presented “some significant questions concerning the voluntariness or general validity of the plea,” United States v. Gonzalez, 970 F.2d at 1100, but it need not hold such a hearing if the movant’s allegations “merely contradict
[his] earlier statements made under oath at his plea allocution,” id. at 1101. The district court’s denial of a motion to withdraw a plea of guilty is reviewed only for abuse of discretion. See, e.g., United States v. Vega, 11 F.3d 309, 313 (2d Cir. 1993); United States v. O’Hara, 960 F.2d 11, 13-14 (2d Cir. 1992).
 Mancusi and Giordano, in support of their motions to withdraw their respective pleas of guilty, argued principally that they did not understand the charges, that they were innocent, and that the evidence submitted by the government at the aborted trial was insufficient to convict them. Giordano submitted to the court documents and affidavits from his codefendants and others to support his contention that he was innocent. The court
properly rejected the claims of lack of understanding for the reasons discussed in Part II.A. above, and, given the standards discussed below, it plainly did not abuse its discretion in rejecting defendants’ claims of innocence and insufficiency of the evidence.
 It is well established that a defendant who challenges the sufficiency of the evidence to support his conviction after a jury verdict bears a heavy burden. In reviewing such a challenge, an appellate court is required to view the evidence, “whether direct or circumstantial, in the light most favorable to the government, crediting every inference that could have been drawn in its favor,” United States v. Gordon, 987 F.2d 902, 906 (2d Cir. 1993), and to deem the evidence sufficient if “any rational trier of fact could have found the essential elements of the crime,” United States v. Rivera, 971 F.2d 876, 890 (2d Cir. 1992) (internal quotation marks omitted) (emphasis in original). The same standard is applicable to a district court reviewing a motion for a judgment of acquittal. See generally Jackson v. Virginia, 443 U.S. 307, 318-19 (1979); United States v. Taylor, 464 F.2d 240, 243 (2d Cir. 1972); 2 C. Wright, Federal Practice and Procedure Section(s) 467, at 658-65 (1982); id. at 663-65 (“It is not for the [district] court to assess the credibility of witnesses, weigh the evidence or draw inferences of fact from the evidence. . . . The court must . . . take the view of the evidence and the inferences therefrom most favorable to the government.” (footnotes omitted)).
 The burden of a defendant who has been convicted after pleading guilty, and who contends thereafter that he should be allowed to withdraw his plea because he is innocent, is plainly no less heavy. The self-inculpatory statements he made under oath at his plea allocution “carry a strong presumption of verity,” Blackledge v. Allison, 431 U.S. at 74, and the court, in reviewing the belated claims of innocence, must draw all permissible inferences in favor of the government and against the defendant, especially when, as here, the defendant has gone to trial, heard most of the government’s evidence, and then pleaded guilty, describing his wrongdoing and acknowledging that he could not effectively defend against that evidence.
 The defendants here have not met their burden, for the district court was, in all the circumstances, entitled to reject the newly advanced innocent explanations for their behavior and to credit instead the evidence that had been presented at trial and in the defendants’ own earlier descriptions of their conduct. For example, Giordano’s motion, surprisingly asserting that “Mr. Giordano always has maintained his innocence” (Affidavit of David I. Schoen dated May 22, 1996 (“Schoen Aff.”), at 3), claimed that Mancusi had obtained the funds in question in Hong Kong legitimately from Korean investors. Yet Giordano himself, in pleading guilty had said, “I with other people gave Mr. Mancusi money to transport to Hong Kong which I believed came from illegal sources, . . . I believed it was illegal sources.” (Tr. 1175-76.) And though Giordano’s new contention was that the money was meant for lawful investments in Liberia, at his plea allocution he had stated that the purpose of the Hong Kong deposits was “[t]o conceal the source of the money.” (Tr. 1176.) Giordano’s own allocution thus contradicted virtually every aspect of the explanation advanced in his motion. In addition, his motion proffered, inter alia, a lengthy affidavit from Mancusi supporting Giordano’s description of the Korean-investors explanation. Yet Mancusi did not submit such an affidavit in support of his own motion to withdraw his plea, and in his own plea allocution, Mancusi had said: I transported money from the United States to Hong Kong, and there I deposited in a savings account, and from that point that savings account was used, unbeknownst to me, but for illegal profit, and that’s what occurred for myself and Mr. Giordano.
 (Tr. 1154.) Mancusi, noting that he had been given a total of more than $7 million to take to Hong Kong with only a single slip of paper bearing the name of a savings account, said in his plea allocution that though he did not know the money came specifically from narcotics trafficking, “I wasn’t a moron”; “I illegally transported funds which I felt were
illegal, gained by illegal enterprise.” (Tr. 1155.)
 The district judge, who had addressed each defendant individually in conducting the plea inquiries and who had had the opportunity to observe their demeanor and assess their credibility, was plainly entitled to reject the belated claims of innocence that contradicted their credible pleas of guilt. And though Giordano’s motion argued that despite the government’s documentary evidence, there were “alternative noninculpatory possibilities” (Schoen Aff. at 8), the district court properly drew all permissible inferences in favor of the government. The court did not abuse its discretion in denying the motions of Mancusi and Giordano to withdraw their pleas of guilty on the ground that they were actually, or could conceivably be found to be, innocent. Mancusi and Giordano also contend that they should have been allowed to withdraw their pleas because they had received ineffective assistance of counsel. We reject these contentions substantially for the reasons stated by the district court in denying the motions.
 E. Sentencing
 Mancusi and Giordano also challenge their sentences. Their challenges are not properly before us because they have been waived. In their respective plea agreements, defendants stipulated to various offense levels under the Guidelines and acknowledged various sentencing ranges that would be applicable with respect to those offense levels in light of their respective criminal history categories. To the extent pertinent here, defendants further agreed not to appeal “any sentence within or below the stipulated Guidelines range[s].” With respect to Mancusi, the pertinent stipulated range was 108-135 months’ imprisonment; he was sentenced to 108 months. With respect to Giordano, the pertinent stipulated range was 121-151 months’ imprisonment; he was sentenced to 151 months.
 “In no circumstance . . . may a defendant, who has secured the benefits of a plea agreement and knowingly and voluntarily waived the right to appeal a certain sentence, then appeal the merits of a sentence conforming to the agreement.” United States v. Salcido-Contreras, 990 F.2d 51, 53 (2d Cir.) (per curiam) (dismissing appeal), cert. denied, 509 U.S. 931 (1993); see United States v. Rivera, 971 F.2d at 896. Accordingly, we decline to address their sentencing contentions.
 We have considered all of defendants’ contentions on these appeals and have found them to be without merit. The judgments of conviction are affirmed.