
    UNITED STATES of America, Plaintiff-Appellee, v. Antonino CUSIMANO and Philip Ducato, Defendants-Appellants.
    Nos. 97-1186, 97-1187 and 97-2786.
    United States Court of Appeals, Seventh Circuit.
    Argued March 31, 1998.
    Decided July 1, 1998.
    
      Duane J. Deskins (argued), Office of the United States Attorney, Criminal Division, Chicago, IL, for Plaintiff-Appellee.
    Thomas J. Royee (argued), Chicago, IL, George Pappas, Neville, Pappas & Mahoney, Chicago, IL, for Defendant-Appellant Cusi-mano.
    Carl P. Clavelli (argued), Chicago, IL, for Defendant-Appellant Dueato.
    Before POSNER, Chief Judge, and CUMMINGS and KANNE, Circuit Judges.
   KANNE, Circuit Judge.

Antonino Cusimano and Philip Dueato challenge their convictions for conspiracy to possess with intent to distribute cocaine. Cusimano also challenges his conviction for possession with intent to distribute cocaine. Specifically, both Cusimano and Dueato argue that the district court constructively amended the indictment through its jury instructions. Dueato also argues that the prosecution denied him a fair trial by imper-missibly vouching for the credibility of cooperating witnesses in its closing argument and that the district court erred in denying his motion for a new trial based on newly-discovered evidence. Cusimano alleges that the district court erred in denying his motion to bar the testimony of Victor Bustami, or in the alternative for a new trial. Because we find the defendants’ arguments unpersuasive, we affirm their convictions.

I. History

The details of Dueato’s and Cusimano’s activities that led to their arrest and conviction are not of import to this appeal. We will therefore recite only those facts relevant to their claims on appeal. On January 27,1995, Cusimano and Dueato were arrested for conspiracy to distribute cocaine and possession with intent to deliver cocaine. The arrest was a result of a Drug Enforcement Agency surveillance operation. At trial, the government’s key witness' was Victor Bustami. Bustami had been involved with Dueato and Cusimano as a confidential informant. Bus-tami agreed to work with the DEA and testify against Cusimano and Dueato in exchange for a downward departure in his sentencing for an unrelated drug transaction. In addition to Bustami’s trial testimony, the government also presented tapes of several conversations between Bustami and the defendants. These tapes were played for the jury.

The indictment alleged a conspiracy existing from “on or about January 19, 1995, and continuing until on or about January 27, 1995.” At trial, the district court admitted evidence from outside the indictment period, some of which extended back several years. The government submitted a proffer that explained that the evidence provided necessary background to help the jurors understand the charged conspiracy. The evidence related to the defendants’ relationship, their relationship with Bustami, and their connections to the drug trade.

On the first day of the trial, the defendants learned of evidence that could be used to impeach Bustami’s credibility. Bustami was arrested bringing a car to auction; the owner of the car had reported it stolen. Bustami claimed that he had a lien on the car, that the owner had not made his payments, and that he lawfully possessed the car. In fact Busta-mi did not lawfully possess the car. The DEA agents with whom Bustami was working knew about the arrest and Bustami’s statements but did not disclose this information to the prosecutor until the day of the trial. The prosecutor alerted defense counsel. In light of this evidence and after a preliminary investigation, Cusimano moved the district court to bar Bustami’s testimony because the DEA agents had violated Cusi-mano’s due process rights by failing to turn over the information to the prosecution. This motion was denied by the district court. Post-trial Cusimano renewed his motion to strike or bar Bustami’s testimony and moved in the alternative for a new trial. The district court also denied this motion.

After a ten-day trial, the jury found Cusi-mano guilty of conspiracy to possess with intent to distribute cocaine in violation of 21 U.S.C. § 846 and possession with intent to distribute cocaine in violation of 21 U.S.C. § 841(a)(1). The jury found Dueato guilty only of conspiracy.

After the trial, new evidence regarding the extent of Bustami’s criminal activities came to the attention of the' defendants. While Bustami had testified to being involved with cocaine only, this evidence suggested that on at least one occasion Bustami had delivered heroin for his uncle. Given this new evidence, Ducato moved for a new trial. The district court denied this motion.

This appeal followed.

II. Analysis

A. Constructive Amendment of the Indictment

Cusimano and Ducato contend that the evidence introduced at trial and the district court’s instructions to the jury amounted to a constructive amendment of the indictment. While not directly challenging the district court’s decision to admit evidence of the defendants’ relationship prior to the time frame in the indictment, Cusimano and Ducato claim that the admission of this evidence, coupled with the “other acts” instruction, the conspiracy instruction, and the lack of a limiting instruction, resulted in the possibility that they were convicted of a conspiracy other than the one that allegedly existed during the time frame stated in the indictment.

Because Cusimano and Ducato did not raise the constructive amendment issue or object to the jury instructions below, they have waived the objection on appeal. We therefore review for plain error. See United States v. Remsza, 77 F.3d 1039, 1043 (7th Cir.1996); United States v. Leichtnam, 948 F.2d 370, 375 (7th Cir.1991). Under the plain error standard, we will not reverse unless the defendants demonstrate (1) there was error; (2) the error was clear or obvious; and (3) the error affected the defendants’ substantial rights. See United States v. Olano, 507 U.S. 725, 732-35, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993); United States v. Ross, 77 F.3d 1525, 1538 (7th Cir.1996). If the defendants are able to prove these elements, we have the power to correct the error but are not required to do so. Olano, 507 U.S. at 735, 113 S.Ct. 1770. We will not reverse unless we find the error seriously affects the fairness, integrity, or public reputation of judicial proceedings. See id. at 736, 113 S.Ct. 1770; Ross, 77 F.3d at 1538. In the context of constructive amendment claims, we have previously held that “[i]n the context of plain error review, the amendment must constitute ‘a mistake so serious that but for it the [defendant] probably would have been acquitted’ in order for us to reverse.” Remsza, 77 F.3d at 1044 (quoting United States v. Gunning, 984 F.2d 1476, 1482 (7th Cir.1993)).

“A constructive amendment to an indictment occurs when either the government (usually during its presentation of evidence and/or its argument), the court (usually through its instructions to the jury), or both, broadens the possible bases for conviction beyond those presented by the grand jury.” Floresca, 38 F.3d at 710. The introduction of evidence of pre-conspiratorial events does not by itself create a constructive amendment to the indictment. See United States v. Spaeni, 60 F.3d 313, 315 (7th Cir.1995). As we explained in Spaeni:

[T]his circuit has a well-established line of precedent which allows evidence of uncharged acts to be introduced if the evidence is “intricately related” to the acts charged in the indictment. See, e.g., United States v. Ramirez, 45 F.3d 1096, 1102 (7th Cir.1995). Under this doctrine, evidence of uncharged criminal activity is admissible to provide the jury with a complete story of the crime on trial, to complete what would otherwise be a chronological or conceptual void in the story of the crime, or to explain the circumstances surrounding the charged crime. See id. and cases cited therein.

60 F.3d at 316. Therefore, Cusimano and Ducato focus their challenge on the jury instructions. They assert that the instruction on “other acts evidence,” the conspiracy instruction, and the lack of a limiting instruction effectuated the constructive amendment.

We first note that under the “intricately related” doctrine, the court is not required to give a limiting instruction at the time of the admission of evidence or as part of the charge to the jury. See United States v. Akinrinade, 61 F.3d 1279, 1286 (7th Cir.1995). Since the court has no duty to offer an instruction sua sponte, it cannot be faulted for not giving an instruction absent a request to do so. Here, appellants did not ask the court for a limiting instruction and therefore their argument for error on this point is unpérsuasive.

We also find no plain error with regard to the jury instructions. Cusimano and Ducato challenge the “other acts” instruction because it contained no reference to the dates contained in the indictment. While they do not make this argument explicitly, when, read in conjunction with their constructive amendment claim Cusimano and Ducato must argue that the instruction permitted the jury to convict them for their acts prior to the conspiracy alleged in the indictment. The instruction in question that was provided to the jury and orally given reads as follows:

You have heard evidence of acts of the defendants other than those charged in the indictment. You may consider this evidence only on the question of whether the conspiracy charged in the indictment existed and whether each defendant was a member of that conspiracy. This evidence is to be considered by you only for this limited purpose.

Tr. at 1498 (emphasis added). Given that the instruction states explicitly that the evidence is to be used in evaluating “the conspiracy chai’ged in the indictment,” we fail to see how it created the possibility that the defendants could be convicted for acts outside the period established in the indictment. We therefore find no plain error.

On the conspiracy instruction, appellants argue that it was “confusing” and “contradictory” and invited the jury “to find Philip Ducato [and Cusimano by adoption] to be a member of the conspiracy on the unfair assumption that his prior conduct and relationships with Cusimano and his uncle intimated a propensity to commit drug crimes from their acts and statements.” Ducato Br. at 24. We find it difficult to articulate the error alleged here. However, we assume that appellants are concerned that they may have been convicted of the conspiracy alleged in the indictment based only on the evidence from outside the indictment period, and evidence of the acts and statements of others. The part of the conspiracy instruction at issue that was orally given to the jury reads as follows:

In determining whether the alleged conspiracy existed, and whether a defendant— and whether a defendant became a member of the conspiracy, you may consider the acts and statements of all the alleged participants. The agreement may be inferred from all the circumstances and the conduct of all the alleged participants.
Only the defendant’s own words and acts show whether the defendant joined the conspiracy. You may consider [state-merits] by other persons in deciding what the defendant did and said or to help you understand a defendant’s acts or statements.

Tr. at 1503. The allegedly “confusing” aspect of the instruction is that initially the jury is told that it may consider acts and statements of all of the alleged participants to determine whether a defendant became a member of the conspiracy, yet later the jury is told that only the defendant’s own words and conduct show whether he joined the conspiracy. But neither the written nor the oral instruction ends there. They then explain how the jury could use acts and statements of the other participants in making the determination about whether a defendant joined the conspiracy. We do not find this instruction so confusing as to rise to the level of “plain error.” Additionally, it is unlikely that the jury could have heard or read this instruction and then convicted the defendants for a crime that fell outside the period alleged in the indictment; the instruction specifically makes reference to “the alleged conspiracy,” i.e. the conspiracy alleged in the indictment.

Because we find that the court need not have issued a limiting instruction, and that the instructions as given both orally and in writing did not rise to plain error, we hold that the indictment was not constructively amended. Our conclusion is bolstered by the fact that the district court instructed the jury that Cusimano and Ducato were on trial for the charges made in the indictment, that it was to give separate consideration as to each count in the indictment and as to each defendant, and that the evidence must establish that the offense was committed on a date reasonably near the date charged. The district court also provided the jury with a copy of the indictment. These facts, combined with our finding that there was no plain error in the jury instructions, establish that there was no constructive amendment to the indictment. See United States v. Mitchell, 64 F.3d 1105, 1111-12 (7th Cir.1995) (finding no constructive amendment where court unambiguously instructed the jury on the indictment), cert. denied, 517 U.S. 1158, 116 S.Ct. 1549, 134 L.Ed.2d 651 (1996); United States v. Lopez, 6 F.3d 1281, 1287-88 (7th Cir.1993) (finding no constructive amendment when court instructed .jury that defendant not on trial for any act or conduct not alleged in the indictment and gave the jury copy of indictment).

B. Prosecutor’s Comments During Closing Argument

Ducato argues that the government’s final summation to the jury impermissibly bolstered the credibility of the government’s witnesses. The government accomplished this, Ducato asserts, by “exhorting the jurors to agree and empathize with [the government’s] feeling of personal outrage ... at the alleged unjustified attacks upon these witnesses and the hardworking and honest federal agents who were responsible for the case.” Ducato Br. at 34.

We employ a two-part test for assessing remarks alleged to be improper. First, we determine whether the comments, looked at in isolation, were improper. See United States v. Morgan, 113 F.3d 85, 89 (7th Cir.1997); United States v. Butler, 71 F.3d 243, 254 (7th Cir.1995); United States v. Johnson-Dix, 54 F.3d 1295, 1304 (7th Cir.1995). If the remarks were improper, we then look at the remarks in the light of the entire record to determine whether the defendant was deprived of a fair trial. See Morgan, 113 F.3d at 89; Butler, 71 F.3d at 254; Johnson-Dix, 54 F.3d at 1304. Because Ducato did not object to the statements at the time, we review the prosecutor’s alleged improper remarks for plain error. See United States v. Laurenzana, 113 F.3d 689, 695 (7th Cir.1997), cert. denied, — U.S. -, 118 S.Ct. 240, 139 L.Ed.2d 170 (1997). “The discretion to correct plain error should be employed in those circumstances in which a miscarriage of justice would otherwise result, namely, in those cases in which the error has affected the outcome of the district court proceedings.” Id. (citing United States v. Olano, 507 U.S. 725, 734-36, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)).

Ducato complains about the following language in the prosecutor’s closing argument:

Counsel has spent a great deal of time talking about Mr. Bustami and Mr. Bruno, and they have even used the words we “bought them.” I resent that. We did not buy them. We arrested them. We convicted them, and they are going to stand before judges and be sentenced for their crimes. They are bound by written plea agreements which require them to tell the truth. No truth, no deal, bigger sentence, that is the assurance that you have that they are telling the truth, but there is more.
The agents in this case have been insulted. They’ve been chastised. They’ve been questioned by all three of the attorneys who have argued on behalf of the defendants. It is these agents who have monitored the informants in this case, who have conducted themselves honorably, and it is these men who have presented the case to you. I resent any implication that they have done less than that.

Tr. at 1447,1450.

We will assume, without deciding, that the comments, looked at in isolation, were improper, because we find the second step of the analysis to be determinative. We do not believe that these comments denied Ducato a fair trial or affected the outcome of the proceedings. See Laurenzana, 113 F.3d at 695; Morgan, 113 F.3d at 89. We look to five factors to determine the effect on, the fairness of the trial:

1) the nature and seriousness of the prose-cutorial misconduct; 2) whether the conduct of the defense counsel invited the prosecutor’s remarks; 3) whether the trial court’s instructions to the jury were adequate; 4) whether the defense was able to counter the improper arguments through rebuttal; and 5) the weight of the evidence against the defendant.

United States v. Granados, 142 F.3d 1016, 1021-22 (7th Cir.1998). The prosecutor’s remarks were not egregious. . While commenting on the credibility of the witnesses, such comments were explicitly invited by defense counsels’ attacks on the credibility of the witnesses. Since Ducato raised no objection at the time, the trial court did not instruct the jury specifically in regard to the prosecutor’s comments. However, the court did instruct the jury that closing arguments are not evidence, that the jury decides the credibility of the witnesses,, and that the testimony of some of the government’s witness should be considered with caution and great care. Defense counsel did not have the opportunity to counter the statements through rebuttal, but we are reminded that the statements themselves were in response to defense counsels’ own comments. Finally, the weight of the evidence supports Ducato’s conviction. In light of the above factors, Ducato cannot persuade us that the prosecutor’s remarks deprived him of a fair trial.

Because we review for plain error, Ducato must prove not only that the remarks denied him a fair trial but also that the outcome of the proceeding would have been different absent the remarks. Even if we thought Ducato could sustain the former proposition, the latter falls under the weight of the evidence against him. We therefore find no plain error in the prosecutor’s remarks and decline to grant Ducato relief for this reason.

C. Ducato’s and Cusimano’s Other Arguments

Both Cusimano and Ducato claim on appeal that the district court erred in denying motions based on Bustami’s testimony. Neither defendant’s claim merits significant discussion. Ducato asserts that the district court should have granted his motion for a new trial because, after the trial’s conclusion, he discovered new evidence that could have been used to impeach Bustami. Cusimano claims the court erred by denying his pre- and post-trial motions to strike Bustami’s testimony1 on the ground that the DEA agents with whom Bustami worked violated Cusimano’s due process rights.

In accord with the district court opinion below, we find no merit in Ducato’s arguments. Ducato has not shown that the jury would have reached a different conclusion absent the allegedly false testimony, see United States v. Fruth, 36 F.3d 649, 652 (7th Cir.1994), nor has he established that the newly-discovered evidence was material and not merely impeaching or cumulative, and would probably lead to an acquittal in the event of a new trial, see United States v. Gonzalez, 933 F.2d 417, 447 (7th Cir.1991), We also find no merit in Cusimano’s assertion that the DEA agents’ so-called “suppression” of impeaching evidence violated his due process rights. We therefore find that the district court did not abuse its discretion as to Ducato’s and Cusimano’s motions.

We therefore Affirm Ducato’s and Cusi-mano’s convictions. 
      
      . Cusimano and Ducato also raise the court's failure to guide the jury in its response to a note the jury sent during deliberations as evidence that the indictment was constructively amended. Appellants, however, waived any error by affirmatively approving the wording of the court's response. See United States v. Griffin, 84 F.3d 912, 924 (7th Cir.1996), cert. denied sub nom. Rux v. United States, — U.S. -, 117 S.Ct. 495, 136 L.Ed.2d 387 (1996). Since waiver of this sort extinguishes any error, we decline to address this contention.
     
      
      . Cusimano’s and Ducato’s brief makes passing reference to the district court's alleged error in admitting the evidence in the first instance. "Here the trial judge simply erred in her preliminary ruling on this evidence's admissibility. Unlike those decisions wherein such evidence is directly and 'intricately related' to the charged offense, here the evidence was related to an uncharged offense which preceded the charged conspiracy.” Ducato Br. at 28. To the extent that Cusimano and Ducato intended to raise this issue on appeal, we find they have waived it for failure to develop it on appeal. See United States v. Berkowitz, 927 F.2d 1376, 1384 (7th Cir.1991) ("We have repeatedly made clear that perfunctory and undeveloped arguments ... are waived.”). Even were we to address this issue, we would find it has no merit because "this circuit has a well-established line of precedent which allows evidence of uncharged acts to be introduced if the evidence is 'intricately related’ to the acts charged in the indictment.” United States v. Spaeni, 60 F.3d 313, 316 (7th Cir.1995). Since the uncharged acts filled a chronological and conceptual void regarding the formation, nature, and duration of the relationship between the coconspirators, the district court did not err in admitting the evidence.
     
      
      .We have previously stated that a constructive amendment to an indictment is "reversible per se” or that if we find such an amendment "reversal is automatic.” See, e.g., Leichtnam, 948 F.2d at 377-78 (stating that any broadening of possible bases for conviction beyond those that appear in indictment is "fatal” or "reversible per se,” and if impermissible amendment is found, “reversal is automatic”); United States v. McAnderson, 914 F.2d 934, 944 (7th Cir.1990) (Constructive amendments are prejudicial per se.). Wc do not believe that these prior statements imply that the plain error analysis for the constructive amendment claim is inappropriate. In fact, in Leichtnam, a case employing the aforementioned language, we explicitly stated that we would have used the plain error analysis had the government not waived that argument on appeal. See Leichtnam, 948 F.2d at 375. Additionally, our constructive amendment cases have employed the plain error analysis when it was appropriate to do so. See, e.g., United States v. Feinberg, 89 F.3d 333, 339 (7th Cir.1996), cert. denied, - U.S. -, 117 S.Ct. 997, 136 L.Ed.2d 876 (1997); Remsza, 77 F.3d at 1043 ("A constructive amendment is per se reversible where the defendant raised the proper objections below.... However ... because Remsza objected to neither the evidence nor the jury, instruction in question, he waived the objection on appeal. Therefore, we review for plain error.” (citations and footnote omitted)). Accord United States v. Floresca, 38 F.3d 706, 711-14 (4th Cir.1994) (recognizing that constructive amendments to indictments are error per se, then engaging in plain error analysis because objections had not been preserved below). We note that the Fourth Circuit concluded in Floresca that once a constructive amendment is found, such amendment will always meet the plain error standard as well as our standard governing the exercise of our discretion. See id. at 714. We have not gone so far. See Remsza, 77 F.3d at 1044 (assuming arguendo that constructive amendment occurred, then finding no plain error). But see United States v. Pedigo, 12 F.3d 61-8, 631 (7th Cir.1993) (“[I]f an amendment occurred, the plain error standard of review will not save the conviction.”). Although Cusimano and Ducato invite us to create a blanket rule like that of the Fourth Circuit, we decline to do so. We need not reach the issue of whether constructive amendments of indictments are always reversible because we conclude no amendment occurred.
     
      
      . To the extent that Cusimano and Ducato argue that the instruction was erroneous because it allowed the jury to consider acts outside the indictment period as evidence of their guilt of conspiracy during the time period alleged in the indictment, wc remain unpersuaded. "In deciding whether a defect in a jury instruction is 'plain error,' we must examine the entire record before us, and determine whether the instructional mistake had a probable impact on the jury’s finding that the defendant was guilty." United States v. Brothers, 955 F.2d 493, 496 (7th Cir.1992) (quotations omitted). Our review of the record reveals a substantial amount of evidence from the period alleged in the indictment that would support the jury's verdict. The pre-indictment acts were certainly not necessary for a guilty verdict. Wc therefore find no plain error here.
     
      
      . Although according to the transcripts the oral instruction did not include the word "statements" in the last sentence, this possible omission docs not affect our decision. The jury was given the correct written instructions during deliberations and the failure to include this word in the oral charge does not rise to the level of plain error.
     