ORDER
Police officers in Nebraska discovered 900 pounds of marijuana in an SUV during a traffic stop in September 2006. The driver agreed to cooperate with the DEA and delivered his cargo to Reginald Bick-ham, a marijuana distributor in Milwaukee, Wisconsin. Bickham was arrested and fingered people below him in the distribution chain, including the defendant, Dwayne Toliver, who was arrested in May 2007. The other participants pleaded guilty, but Toliver insisted that Bickham had falsely accused him to curry favor with prosecutors. A jury rejected this defense and found Toliver guilty of conspiracy to distribute marijuana, 21 U.S.C. §§ 846, 841(a)(1). The drug quantity and his criminal history triggered a 10-year statutory minimum, see id. § 841(b)(l)(B)(viii), which the district court imposed. Toliver filed a notice of appeal, but his appointed lawyers move to withdraw because they cannot find a nonfrivolous issue to pursue. See Anders v. California, 386 U.S. 738, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967). Toliver opposes counsel’s submission. See CIR. R. 51(b). We confine our review to the potential issues identified in counsel’s facially adequate brief and Toliver’s response. See United States v. Schuh, 289 F.3d 968, 973-74 (7th Cir.2002).
At trial Bickham testified that he was a small-time distributor until late 2004 when a willing source started fronting him large amounts of marijuana. Initially he received 20-pound shipments from this supplier, but over time the weight increased until reaching the 900 pounds intercepted by police. Bickham did not sell directly to users but instead fronted the drug to dealers who employed their own distributors or sold it themselves. He explained that Toliver, whom he knew only as “Big Baby,” owned the car wash he patronized and sold small amounts of marijuana for him as early as 2]6 to 3 years before the Nebraska seizure. As his drug business grew, Bickham continued, he needed a safe place to transfer the marijuana from the supplier’s car to his, and Toliver let him use the car wash. After that, said Bickham, he began giving Toliver more marijuana to sell, ranging from 5 to 100 pounds. Bick-ham added that Toliver was always present when marijuana was being unloaded at the car wash. Another man, Bickham’s longtime friend Rahjee Shabazz, was also present on occasion. Bickham stopped using the car wash in 2005 but continued fronting marijuana to Toliver until the next year when he failed to pay for 15 pounds worth about $10,000. At that point, said Bickham, he ended all contact with Toliver. Bickham’s cell phone records for 2006 corroborate that he and To-liver conversed more than 170 times in January and February before the calls ceased.
Before his arrest Bickham had been using notebooks and scraps of paper to track his drug business. He gave these ledgers to investigators and explained at trial that he started keeping records when his operation became too big to track mentally. In his ledgers he recorded the weight of the marijuana and the amount of money paid or owed by his customers, who were identified only by initials or nicknames. Their real names were often unknown to him. Bickham testified that Toliver’s transactions were listed under “Big Baby” or “Wash” — the latter a nickname referring to his car wash but that Bickham never used when speaking with Toliver.
*657Shabazz, Bickham’s Mend, also pleaded guilty and testified for the government. He knew Toliver only as “Big Baby” and first met him when Bickham was using the car wash to unload marijuana. Bickham would call Toliver when a shipment arrived, and Toliver would let them into the car wash to unload and weigh the drugs. Bickham fronted part of those shipments to Shabazz and Toliver. Shabazz testified that investigators showed him Bickham’s ledgers and asked if he was the customer identified as “Rha.” He told the jury he assumed that “Rha” was short for Rahjee even though Bickham never called him by that nickname. Shabazz confirmed that the numbers in the ledgers were consistent with amounts of drugs Bickham had fronted him and the money he owed in return. Shabazz also confirmed that the directory copied from his cell phone by police after an unrelated arrest in 2005 included Toliver’s number stored under “Big Baby.”
Four other buyers of Bickham’s marijuana likewise pleaded guilty and testified for the government. One of them knew Toliver socially, but otherwise none was aware that he was buying from Bickham, and neither did they know any of Bick-ham’s other customers. All four, though, recognized in Bickham’s ledgers their own transactions with him.
Toliver took the stand and denied selling drugs. He said he met Bickham in 2005 when Bickham started coming to his car wash 2 or 3 times a week with up to 15 different vehicles. Toliver insisted that he uses the nickname “Man,” which is what Bickham called him, not “Big Baby” or “Wash.” Toliver also acknowledged that Bickham telephoned him frequently, but always concerning his cars. And he in turn called Bickham, he continued, because Bickham had a habit of being late to retrieve his cars. Toliver testified that Bick-ham quit coming to his car wash early in 2006 but did not tell him why.
Other than his own denials, Toliver’s defense relied on cross-examination of the government’s witnesses and his fiancee’s testimony that she never saw him with large quantities of drugs. Defense counsel questioned Bickham about his motivation for testifying and implied that he was lying about Toliver to evade a 10-year statutory minimum and an even-higher imprisonment range under the guidelines. Counsel questioned why Bickham had used two different names for Toliver in his ledgers, but the nicknames of other customers did not vary. Counsel elicited that it took Bickham months to provide enough information for investigators to begin identifying the customers in his ledger entries, and Bickham agreed that he was under pressure “to put a name with every one of those nicknames.” Bickham countered, however, that even at the time of trial there were still a number of ledger entrants who remained unidentified and at large.
In this court both counsel and Toliver consider whether Toliver could tease a nonMvolous issue from the differing dates of the conspiracy alleged in the indictment and proven at trial. The indictment alleges a conspiracy beginning in January 2006 and continuing until the date of Biekham’s arrest in September 2006, but the evidence at trial showed that Toliver and Bickham had engaged in drug transactions beginning in 2005 and continuing through February 2006. Toliver proposes to argue that the government actually proved two conspiracies — one in 2005 involving Bick-ham and Shabazz using the car wash to unload drugs and the other beginning in January or February 2006 — and thus the lack of a multiple-conspiracy jury instruction sullies his conviction. And counsel also examine whether Toliver could argue that the differing time frames led to a constructive amendment of the indictment, *658a fatal variance, or proof insufficient to convict.
All of these contentions would be frivolous. First, the very suggestion that the evidence established two separate marijuana conspiracies would doom the possibility of a constructive amendment: the indictment charges a drug conspiracy, and a constructive amendment, by definition, cannot occur unless the evidence and the jury instructions allowed conviction for an entirely different crime from what the indictment alleges. See United States v. Ratliff-White, 493 F.3d 812, 820 (7th Cir.2007); United States v. Trennell, 290 F.3d 881, 888 (7th Cir.2002); United States v. Johnson, 248 F.3d 655, 665 (7th Cir.2001). The beginning and ending dates of a conspiracy are not elements of the offense, so proof of different dates could never raise the specter of conviction for a different crime. See United States v. Hatten-Lubick, 525 F.3d 575, 581 (7th Cir.2008); United States v. Spaeni, 60 F.3d 313, 315-16 (7th Cir.1995); United States v. Jackson, 935 F.2d 832, 844 (7th Cir.1991). Moreover, on this record we would be compelled to conclude that a rational jury could have found that Toliver knew about and agreed to participate in Bickham’s marijuana business within the dates alleged in the indictment, thus also dooming any claim of variance or insufficient evidence. See United States v. Haynes, 582 F.3d 686, 698 (7th Cir.2009) (discussing variance); United States v. Dean, 574 F.3d 836, 842 (7th Cir.2009) (same); United States v. Longstreet, 567 F.3d 911, 918-19 (7th Cir.) (discussing sufficiency of the evidence), cert. denied, — U.S. -, 130 S.Ct. 652, 175 L.Ed.2d 497 (2009); United States v. Harris, 585 F.3d 394, 402 (7th Cir.2009) (same). Bickham’s testimony established that Toliver knowingly helped him receive and sell marijuana, and Sha-bazz’s testimony corroborated Toliver’s involvement in unloading the marijuana. Toliver painted a different, innocent picture, but the jury was entitled to reject his testimony, and we would not upset the jury’s credibility findings. United States v. Hampton, 585 F.3d 1033, 1041-42 (7th Cir.2009).
Counsel next consider whether To-liver could claim en*or based on the government’s use of a prior conviction to impeach him. Counsel examine whether it prejudiced the jury to hear that Toliver had an 8-year-old conviction for possessing cocaine with intent to distribute. Because Toliver did not object at trial, we would review for plain error. United States v. Williams, 272 F.3d 845, 860 (7th Cir.2001). Federal Rule of Evidence 609 allows the government to submit evidence of a defendant’s prior felony conviction if the conviction occurred within the last 10 years and its probative value outweighs the prejudice to the accused. See United States v. Smith, 454 F.3d 707, 716 (7th Cir.2006). In evaluating whether a conviction satisfies this requirement, a trial court should consider “(1) the impeachment value of the prior crime; (2) the point in time of the conviction and the defendant’s testimony; (3) the similarity between the past crime and the charged crime; (4) the importance of the defendant’s testimony; and (5) the centrality of the credibility issue.” United States v. Gant, 396 F.3d 906, 909 (7th Cir.2005). Here, Toliver’s testimony and credibility were central to the case: either he was lying or Bickham was lying. Thus, although the similarity of the two crimes increased the risk of prejudice, the importance of Toliver’s credibility weighed in favor of admissibility. And the prejudicial effect was lessened because the government confined its inquiry to the type and time of conviction and the court gave the jury a limiting instruction. See United States v. Montgomery, 390 F.3d 1013, 1015-16 (7th Cir.2004). Accordingly, we *659agree with counsel that an argument premised on Rule 609 would be frivolous.
Counsel also assess whether Toliver could challenge several remarks the prosecutor made during closing argument, and Toliver identifies other aspects of the prosecutor’s conduct he thinks deserve review. We evaluate alleged impropriety during closing argument in the context of the record as a whole, United States v. DeSilva, 505 F.3d 711, 719 (7th Cir.2007), and in this case, because no objections were lodged at trial, Toliver would face the additional hurdle of plain-error review, see United States v. Anderson, 450 F.3d 294, 300 (7th Cir.2006).
According to counsel, Toliver might argue from two isolated statements — which together comprise 12 lines in 26 pages of transcribed argument — that the prosecutor misstated the evidence and also injected his personal belief that Bickham and Shabazz were credible. But we would not read into the prosecutor’s words any improper meaning or purpose. Regarding the first statement, which counsel characterize as the prosecutor misrepresenting that Bickham and Shabazz testified directly that Toliver’s involvement ended in February 2006, we disagree with counsel’s interpretation. The prosecutor did not attribute the ending date to either Bickham or Shabazz but rather was summarizing the evidence as a whole: Bickham and Shabazz testified about Toliver’s involvement, which likely ended in February 2006 when the phone calls to and from Bickham stopped. In the second statement, which was delivered in rebuttal, the prosecutor reasoned that if Bickham and Shabazz had lied about Toliver’s involvement, they would have concocted a more damning story. This statement was not only invited by defense counsel’s implication that Toliver was falsely accused, see United States v. Myers, 569 F.3d 794, 799 (7th Cir.2009), but was also an appropriate response to that argument, see United States v. Morris, 498 F.3d 634, 643 (7th Cir.2007); United States v. Clarke, 227 F.3d 874, 884-85 (7th Cir.2000); see also United States v. Vazquez-Rivera, 407 F.3d 476, 483-84 (1st Cir.2005); United States v. Perez-Ruiz, 353 F.3d 1, 9-10 (1st Cir.2003). We agree with counsel, then, that an appellate claim premised on these two statements would be frivolous.
In his Rule 51(b) response, Toliver points to a third passage, which he interprets as implying to jurors that they could safely credit the government’s witnesses because the trial judge ensures that they tell the truth. In fact what the prosecutor conveyed is that the judge has final say in whether to lower a witness’s sentence when the government moves for a reduction in exchange for testimony. A prosecutor may discuss a witness’s plea agreement and highlight the negative consequences for being untruthful, United States v. Alviar, 573 F.3d 526, 542 (7th Cir.2009), cert. denied, — U.S.-, 130 S.Ct. 1312, — L.Ed.2d- (2010), and may also clarify the process by which a criminally involved witness may receive a lower sentence, United States v. Johnson, 437 F.3d 665, 672-74 (7th Cir.2006); United States v. Anderson, 303 F.3d 847, 855-56 (7th Cir.2002). Toliver’s proposed argument would be frivolous because, on this record, we would conclude that the prosecutor’s remarks fairly answered To-liver’s theme that his accusers were lying to get a lower sentence.
Finally, Toliver argues that the prosecutor violated the “advocate-witness rule,” which bars an attorney from acting as both witness and advocate in the same proceeding. Toliver singles out two parts of trial. First, it was evident from the prosecutor’s questioning of Bickham that the two men had met when Bickham first started cooperating. Second, during clos*660ing argument the prosecutor repeatedly used the word “we” in acknowledging that the evidence against Toliver was largely testimonial, e.g., the prosecutor explained that “we” did not have recordings of telephone calls and had not caught anyone “in the act” except Bickham. Toliver proposes to argue that these remarks were tantamount to testifying as a witness, but that contention would be frivolous. The questioning of Bickham was entirely proper, see United States v. Watson, 87 F.3d 927, 931-32 (7th Cir.1996); United States v. Marshall, 75 F.3d 1097, 1106 (7th Cir.1996), and although such references to “we” might run the danger of being misinterpreted as vouching for the integrity and good faith of the investigators’ efforts, see United States v. Hermanek, 289 F.3d 1076, 1097-99 (9th Cir.2002), it would be a stretch to draw that inference here, especially given the limitations of review for plain error.
The last two points counsel identify require little discussion. After reviewing the evidentiary objections Toliver made at trial (three for speculation, one hearsay, and one for foundation), we are convinced that it would be frivolous to challenge the rulings. Even if the district court did err in overruling the objections, the testimony and exhibit were so tangential to Toliver’s guilt or innocence that we would find the error harmless. Finally, as counsel notes, Toliver was sentenced to the statutory minimum, so an appeal of his prison sentence would be frivolous.
Accordingly, we GRANT counsel’s motion to withdraw and DISMISS the appeal.