OPINION
MOORE, Circuit Judge.Defendant-Appellant Benjamin Vazquez (‘Vazquez”) was convicted of conspiracy to distribute and to possess with intent to distribute cocaine in violation of 21 U.S.C. § 846. He now appeals his conviction and sentence, arguing (1) that an alleged constructive amendment of the indictment requires the reversal of his conviction and (2) that the district court erred in making adjustments to his base offense level. Because these claims lack merit, we AFFIRM Vazquez’s conviction and sentence.
I
Between 1998 and 1999, Vazquez participated with Roberto Guilfu (“Guilfu”) and Antonio Sanchez (“Sanchez”), among others, in a conspiracy to distribute cocaine in the Cleveland, Ohio, area. On August 25, 1999, the United States (“Government”) filed a nineteen-count indictment against Vazquez and eleven co-defendants. Vazquez was charged with three counts: Count One, for conspiracy to distribute and to possess with intent to distribute cocaine, in violation of 21 U.S.C. § 846, and Counts Nine and Ten, for use of a communication facility in furtherance of a drug trafficking offense, in violation of 21 U.S.C. § 843(b).1 Among the overt acts listed in Count One were (1) a telephone conversation on November 7, 1998, during which Guilfu mentioned Vazquez and (2) the possession on December 14, 1998, of approximately twelve kilograms of cocaine by two co-defendants. Vazquez pleaded not guilty and, after various continuances and changes of counsel, proceeded to trial, where he was convicted of Count One. Although Vazquez objected to a jury instruction requiring a determination of the amount of cocaine for which he was responsible, the jury specifically found that Vazquez conspired to distribute more than five hundred grams but less than five kilograms of cocaine. On February 20, 2001, the district court sentenced Vazquez to 121 months’ imprisonment and a four-year term of supervised release; it also ordered a special assessment of $100. This timely appeal followed.
II
A
Vazquez first argues that the district court constructively amended the indict*552ment in violation of the Fifth Amendment “by allowing the Government to prove and instructing the jury regarding a quantity of drugs not alleged in the indictment, thereby subjecting [him] to a harsher range of punishment.” Appellant’s Br. at 13. As noted above, Count One of the indictment charged Vazquez and his co-defendants with a cocaine conspiracy; it also specified as an overt act of the conspiracy that two of Vazquez’s co-defendants had possessed approximately twelve kilograms of cocaine. Vazquez contends that the attribution in the jury instructions and verdict forms of specific drug quantities to him personally constituted a constructive amendment of the indictment.
We have recently summarized the case-law on constructive amendments:
The Fifth Amendment guarantees that an accused be tried only on those offenses presented in an indictment and returned by a grand jury. The constitutional rights of an accused are violated when a modification at trial acts to broaden the charge contained in an indictment. A variance [to the indictment] occurs when the charging terms [of the indictment] are unchanged, but the evidence at trial proves facts materially different from those alleged in the indictment. In contrast, an amendment involves a change, whether literal or in effect, in the terms of the indictment. This Circuit has held that a variance rises to the level of a constructive amendment when the terms of an indictment are in effect altered by the presentation of evidence and jury instructions which so modify essential elements of the offense charged that there is a substantial likelihood that the defendant may have been convicted of an offense other than that charged in the indictment. The defendant has the burden of proof on this issue.
United States v. Chilingirian, 280 F.3d 704, 711-12 (6th Cir.2002) (internal citations and quotations omitted). We review de novo the question whether an indictment was constructively amended. Id. at 709.
In this case, the indictment charged Vazquez and his co-defendants with a cocaine conspiracy that involved at least twelve kilograms of cocaine,2 which would have violated 21 U.S.C. § 841(b)(1)(A).3 That Vazquez was not personally charged with a specific quantity does not necessarily mean that a variance or constructive amendment occurred when the Government’s evidence at trial and the jury instructions referenced quantities, including the four kilograms of cocaine that he delivered on November 28, 1998. Even if Vazquez can show a variance between the indictment and the proof at trial, which focused on the November 28 delivery de*553tailed in the bill of particulars, we are not persuaded that it is substantially likely that Vazquez was convicted of an offense other than the one charged in the indictment. Vazquez was charged with a § 841(b)(1)(A) cocaine conspiracy and convicted of the lesser-included offense of a § 841(b)(1)(B) cocaine conspiracy. See FED. R. CRIM. P. 31(c). Because the essential elements of the former necessarily include those of the latter, we hold that the indictment was not constructively amended and affirm Vazquez’s conviction.
B
Vazquez’s base offense level was initially calculated at 30 (for at least three-and-one-half but less than five kilograms of cocaine), then increased by two points for obstruction of justice, resulting in a total offense level of 32. With a criminal history category of I, Vazquez’s sentencing range was 121 to 151 months. The district court sentenced him to 121 months. Vazquez now argues that the district court erred at sentencing by (1) neglecting to make findings of fact independent of the jury’s guilty verdict to support the obstruction of justice enhancement under U.S. Sentencing Guidelines Manual (“U.S.S.G.”) § 3C1.1 (2000) and (2) refusing to apply the “safety valve” provision at 18 U.S.C. § 3553(f) and U.S.S.G. § 5C1.2. We review the district court’s interpretation of the Sentencing Guidelines de novo and its factual findings for clear error. United States v. O’Dell, 247 F.3d 655, 674 (6th Cir.2001).
1
• Under U.S.S.G. § 3C1.1, a district court may enhance by two levels the sentence of a defendant who “willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice during the course of the investigation, prosecution, or sentencing of the instant offense of conviction,” so long as “the obstructive conduct related to (i) the defendant’s offense of conviction and any relevant conduct; or (ii) a closely related offense.” Id. The accompanying commentary includes perjury as obstructive conduct. U.S.S.G. § 3C1.1 commentary, applic, notes 2, 4.
In United States v. Dunnigan, 507 U.S. 87, 113 S.Ct. 1111, 122 L.Ed.2d 445 (1993), having defined perjury as the giving of “false testimony concerning a material matter with the willful intent to provide false testimony, rather than as a result of confusion, mistake, or faulty memory,” the Supreme Court required a district court enhancing a defendant’s sentence under § 3C1.1 for perjury to “review the evidence and make independent findings” of such obstructive conduct. Id. at 94-95, 113 S.Ct. 1111. The Dunnigan Court advised district courts “to address each element of the alleged perjury in a separate and clear finding,” but stated that “a finding of an obstruction of, or impediment to, justice that encompasses all of the factual predicates for a finding of perjury” would be sufficient. Id. at 95, 113 S.Ct. 1111. We have interpreted Dunnigan as requiring the following of a district court applying § 3C1.1: “first, it must identify those particular portions of the defendant’s testimony that it considers to be perjurious, and second, it must either make specific findings for each element of perjury or at least make a finding that encompasses all of the factual predicates for a finding of perjury.” United States v. Mise, 240 F.3d 527, 531 (6th Cir.2001) (quotation omitted).
In this case, the district court was initially and seriously concerned about the implications of the jury’s guilty verdict for the truthfulness of Vazquez’s testimony:
[The Guidelines commentary] specifically says that I would have to make a determination that there was a willful *554attempt to obstruct justice ... The problem here ... is that ... [Vazquez] just categorically denied dealing, distributing, selling cocaine during this conspiracy. There’s—this can’t be an accurate testimony or statements that might result from confusion, mistake or faulty memory.
We’re talking about an application—in application number 1, the jury could only conclude that that was a deliberate, willful, false statement under oath by your client if they found him guilty.
I’m not talking about a few of the other details about when someone might have been shopping or not. I certainly wouldn’t consider applying [the] obstruction of justice[ ] enhancement for those things, but I am talking about the— basic statements of your client that he wasn’t a drug dealer during this conspiracy and he denied any knowledge or responsibility for the specific transactions that were imputed to him by the other witnesses.
He specifically denied; he said I’m not a drug dealer. He said I didn’t deliver or distribute any cocaine to any of these people at all. I think he even went so far as to say anyone else.
Obviously if [Vazquez] was innocent and the jury wrongfully convicted him, well, then his testimony wouldn’t be false.
But I was looking at it the other way. On the assumption that the jury’s verdict was correct, is there any argument that ... [Vazquez]’s testimony is not perjurious?
The point is this guideline has got to mean something, so we’re here. If I thought that the ... verdict was inconsistent, so inconsistent with the evidence as to be[] invalid, I would grant [defense counsel’s] motion before or after the verdict. So I will have to accept— we have to accept the verdict.
Joint Appendix (“J.A.”) at 807-10. Ultimately, however, the district court found “from listening and watching Mr. Vazquez on the stand that he did commit perjury when he specifically denied not only involvement in this conspiracy but denied being a drug dealer at all.” J.A. at 819.
We think that the district court sufficiently explained and supported the obstruction of justice enhancement. First, the district court identified as false Vazquez’s denials of involvement in the conspiracy and drug dealing in general. This testimony concerned the material matter of Vazquez’s culpability for the offense charged. Second, by stating that Vazquez’s denials could not be “accurate testimony or statements that might result from confusion, mistake or faulty memory,” the district court made a finding that encompassed all of the factual predicates for a finding of perjury as defined in Dunnigan. We therefore hold that the district court did not commit reversible error in enhancing Vazquez’s sentence for obstruction of justice.
2
Pursuant to 18 U.S.C. § 3553(f) and U.S.S.G. § 5C1.2, a district court may impose a sentence less than the statutory minimum for a drug offense if certain requirements are satisfied. The Government concedes that Vazquez meets four of the five criteria. The fifth requirement provides that “not later than the time of the sentencing hearing, the defendant [must have] truthfully provided to the Government all information and evidence the defendant has concerning the offense or offenses that were part of the same course of conduct or of a common scheme or *555plan.” U.S.S.G. § 501.2(6) (noting that a determination of compliance is not precluded by “the fact that the defendant has no relevant or useful other information to provide or that the Government is already aware of the information”). The defendant bears the burden of proving that he is entitled to a “safety valve” reduction of his total offense level. O’Dell, 247 F.3d at 675.
In this case, the district court observed at sentencing that Vazquez had provided no information to the Government. When Vazquez claimed not to have any information to give, the district court stated:
The point is, Mr. Vazquez, if you have no information because you’re innocent, then, you know, you were wrongfully convicted. If you’ve been convicted[,] to qualify for the safety valve provision, you have to ... provide all the information you have.
And I can only conclude since, I’ve accepted the jury’s verdict, that you haven’t provided all the information at your disposal. Again, if I ... accept what you’re saying, you shouldn’t be sentenced at all. You’re innocent. So I can only read this safety valve provision 5C.
And the Defendant acknowledged his guilt and provided whatever information he or she has. So I have determined that essentially a person such as yourself who—you know, maintains his opinions which of course is your constitutional right to do and goes to trial and testifies and is convicted can’t get the safety valve provision. That’s how I read it.
J.A. at 813-14. Vazquez contends that the district court’s determination amounts to an incorrect legal conclusion “that a person who goes to trial and is convicted, but still maintains his innocence, cannot, as a matter of law, qualify for the safety valve reduction.” Appellant’s Br. at 31.
We do not agree. To be eligible for the safety valve provision, a defendant must “truthfully provide[ ] to the Government all information and evidence the defendant has concerning the offense or offenses that were part of the same course of conduct or of a common scheme or plan.” U.S.S.G. § 501.2(5). We have previously read the provision as “clearly requiring] an affirmative act by the defendant.” United States v. Adu, 82 F.3d 119, 124 (6th Cir.1996). In this case, the district court specifically found that Vazquez had not provided “all the information at [his] disposal.” J.A. at 813. Indeed, the record does not indicate that Vazquez provided to the Government any information at all about himself or his co-conspirators. Cf. O’Dell, 247 F.3d at 675.4 Because *556Vazquez has not carried his burden of proving eligibility for exemption from the statutory minimum sentence, we hold that the district court did not commit reversible error in refusing to apply the safety valve provision.
CONCLUSION
For the foregoing reasons, we AFFIRM the decision of the district court.
. Counts Nine and Ten were later dismissed.
. Vazquez himself was named in only one of the overt acts listed in Count One, which did not charge him with a specific quantity. On November 6, 2000, defense counsel filed a motion for a bill of particulars specifying the amount of cocaine for which Vazquez was allegedly responsible. On November 15, 2000, the Government provided a bill of particulars that alleged (1) that in July or August 1998 Guilfu had advanced six to seven kilograms to Vazquez on credit and (2) that on November 28, 1998, Vazquez had delivered four kilograms of cocaine to Guilfu at Sanchez's garage. The Government also alleged that Vazquez's participation in the overall conspiracy encompassed a December 1998 shipment of twelve kilograms of cocaine to Guilfu and "the distribution of multiple kilograms of cocaine on a weekly and monthly basis for at least ten months.” Joint Appendix ("J.A.”) at 297. Vazquez received the bill of particulars three weeks before trial.
. We note that defense counsel read the indictment as charging a violation of 21 U.S.C. § 841(b)(1)(A) even before the Government provided the bill of particulars.
. Vazquez relies heavily on United States v. Sherpa, 110 F.3d 656 (9th Cir.1996), where the district court applied the safety valve provision to a "culturally sheltered" professional trekker from Nepal who agreed to transport a suitcase from Thailand to the United States. Id. at 658, 663. Customs agents found the suitcase to contain three kilograms of 87% pure heroin, and the defendant was ultimately convicted of possession of heroin with intent to distribute and importation of heroin. Id. at 658. In affirming the reduction of the defendant’s offense level under the safety valve, the Ninth Circuit observed that the defendant "provided the authorities with substantial information concerning the offense, including the names of those involved abroad," while maintaining that he was innocent of knowing the contents of the suitcase. Id. at 663. Vazquez has not so cooperated with the Government. Cf. United States v. Garcia-Sanchez, 189 F.3d 1143, 1150 (9th Cir.1999) (holding that the defendant was not eligible for the safety valve provision because "[h]e never even met with the government to offer information” and suggesting that "[g]iven his undisputed association with members of the conspiracy, he would have some, perhaps useless, relevant information to provide the gov*556ernment even if he were innocent of drug dealing himself").