CUDAHY, Circuit Judge.
Appellants, Buford and Bennie Peak, were convicted of conspiring to possess with intent to distribute marijuana and cocaine, in violation of 21 U.S.C. § 846. They appeal their convictions on a variety of grounds. In their consolidated brief on appeal, Buford and Bennie contend that the district court committed reversible error by giving the jury a supplemental instruction while it was deliberating and by unduly restricting the cross-examination of the government’s key witness. In his separate pro se briefs, Bennie argues that there was reversible error in excluding hearsay statements of Bennie’s state of mind and in refusing to give Bennie’s proposed instruction on his “capture” theory of defense, and that his due process rights were violated when the government knowingly used perjured testimony to obtain his conviction. The Peaks also submitted a reply brief adopting the issues raised by Buford and Bennie separately. Here, Buford adopted Bennie’s pro se contention that his due process rights were violated by the government’s knowing use of perjured testimony.
We affirm Buford’s conviction, reverse Bennie’s conviction and remand Bennie’s case for a new trial.
I.
On July 22, 1986, Buford Peak posted $100,000 in property to get Robert Hackney out of jail. Why Buford did this is a matter of dispute. The prosecution claimed that Buford wanted Hackney to get him large quantities of marijuana and cocaine. Buford said he wanted to engage in legitimate business transactions with Hackney. The day before his release, Hackney agreed to cooperate with members of the Indiana State Police in its investigation of Buford Peak. For about a week, Buford and Hackney engaged in a series of telephone conversations in which they discussed the purchase of drugs. Buford also spoke with his brother, Bennie, during this time. The drug transaction was scheduled to take place on July 30, 1986. Hackney and Gary Alter, a Drug Enforcement Agency (“DEA”) agent posing as Hackney’s source of marijuana and cocaine, were to meet Buford and Bennie at the Peaks’ store.
In the early morning of July 30, Buford told Hackney in a telephone conversation that the deal would be delayed because the people with the money had not arrived yet and because a “tester” had not been found. Buford told Hackney to call Bennie. Instead, Alter called Bennie, and Bennie said that the money was ready and that they would go to the Peaks’ store as soon as they could find someone to test the drugs.
By early afternoon, Bennie had not yet arrived at the store, where Hackney, Alter and Buford were waiting. Buford and Alter began arguing, whereupon Buford grabbed Alter and pulled him to the door. Special agents then arrested Buford and other co-defendants. Bennie was later arrested on a highway driving away from the store.
Buford argued at trial that it was his intent to “capture” Hackney because he was concerned that Hackney would cause him to forfeit his bond. According to Buford, Hackney had initiated the drug deal. Buford claims that he merely played along with Hackney’s idea. To safeguard his bond and possibly to earn a reward, he planned to lure Hackney and his suppliers [828]*828to the Peaks’ store and arrest them when they unloaded the drugs. He claims that he bought a gun and handcuffs for this purpose and that he called Bennie for help in carrying out the plan.
Bennie’s sole defense was that he intended to help Buford carry out the capture plan. His conversations with Hackney and Alter allegedly were designed to stall them, enabling Buford to succeed in his attempt to arrest Hackney. Bennie did not testify, but he offered into evidence Buford’s testimony of his phone conversation with Bennie. The district court, however, refused to admit Bennie’s half of the conversation in which he agreed to help Buford make his capture. The district court also refused to instruct the jury as to Bennie’s capture theory. This ruling was apparently attributable to a lack of evidence to support Bennie’s capture defense. The court did instruct the jury with respect to Buford’s capture theory of defense.
After a week-long trial, at 3:08 a.m. on a Saturday, the district judge, without having received any question from the jury, gave the jury Instruction No. 32, which read:
Members of the jury, as previously stated to you in these instructions, you are to return separate verdicts as to each defendant in each count. However, if you reach unanimous agreement as to any defendant on a count or counts, you may return your verdict or verdicts as to such defendant, defendants, count, or counts when you see fit, and continue your deliberations as to the remainder. You are not required to report all of your verdicts at the same time, although you may do so if you prefer.
If you are unable to reach agreement as to guilt or innocence of a defendant as to a count or counts, you may so state in open court.
Nineteen minutes later, the jury convicted Buford and Bennie of conspiring to possess with intent to distribute illegal drugs.
II.
On appeal, Buford and Bennie argue that Instruction No. 32 had a coercive effect on the jury. They claim that the jury must have been having trouble reaching a verdict because it had been deliberating for several hours. Only nineteen minutes after receiving the instruction the jury announced its guilty verdict. The Peaks contend that this demonstrates that Instruction No. 32 was a “dynamite instruction” that improperly induced the verdicts.
In our view, giving Instruction No. 32 was probably inadvisable. Even the parties agreed that a portion of it could have been interpreted as “nudging” the jury. Counsel for defendants and the government all objected to the instruction. In fact they offered an alternative, which the court rejected. In addition, there was apparently no real need to give Instruction No. 32. The jury, despite deliberating for over four hours, had not sent back word that it was deadlocked or that it needed further guidance.
Nevertheless, we are not convinced that this instruction can fairly be characterized as an “Allen charge” or as a “dynamite instruction,” intended to explode the deadlocked jury into rendering a hurried verdict.1 In fact, the instruction might have [829]*829had the opposite effect. It requested the jury to return verdicts individually as to each defendant and each count. This might have encouraged the jury to organize its deliberations and take its time with each verdict. Instead of pressuring the jurors, the instruction permitted them to acknowledge their inability to reach verdicts as to any defendant or any count. The instruction did not encourage them to make compromises as does an Allen charge. In addition, the instruction was not mandatory; it merely offered the jury an option.
This situation is unlike both United States v. Silvern, 484 F.2d 879 (7th Cir.1973), and United States v. Allen, 797 F.2d 1395 (7th Cir.), cert. denied, 479 U.S. 856, 107 S.Ct. 196, 93 L.Ed.2d 128 (1986), cases in which juries appeared unable to reach verdicts.2 Silvern involved a supplemental instruction designed to break a deadlocked jury. The instruction in our case did not address a deadlock. It related primarily to the complexities of the case and to the hour of the day when the jury was deliberating. Therefore, the court was not required to follow the mandatory procedure outlined in Silvern.
Allen is also inapposite because in that case the court sent instructions to the jury in response to a communication from the jury. Here, the jury had not communicated anything to the judge to prompt the supplemental instruction.
Perhaps the most questionable aspect of this stage of the proceedings is that the jury was deliberating at 3:00 a.m. on Saturday after a long week of trial. But Buford and Bennie have not claimed this as a sepa[830]*830rate basis of appeal apart from the questioned instruction, and we therefore need not decide whether the scheduling of jury deliberations alone is grounds for reversal. Cf. United States v. Murvine, 743 F.2d 511, 515 (7th Cir.1984), cert. denied, 469 U.S. 1190, 105 S.Ct. 962, 83 L.Ed.2d 967 (1985).
III.
Buford and Bennie further contend that the district court violated their sixth amendment right of confrontation by unduly restricting their cross-examination of the government’s key witness, Robert Hackney. Specifically, they argue that the district court deprived them of a fair trial in refusing to allow them to ask Hackney whether he had a valid pilot’s license and in refusing to permit them to question Hackney about his convictions that were more than ten years old.
As to both matters, however, appellants’ contentions do not find support in the record. The district court never prevented them from continuing their cross-examination of Hackney about a valid pilot’s license. The prosecution, in fact, had not objected to this line of questioning. The court simply stated, quite properly, after extensive cross-examination, “I would prefer that we not spend forever on purely collateral matters.” Transcript at 126. In this connection, the subject was of doubtful relevance. In response to the court’s comment, defense counsel voluntarily switched to another subject without even explaining why he had been questioning Hackney about a pilot’s license.
The district court did make an evi-dentiary ruling prohibiting cross-examination on Hackney’s ten-year-old convictions. This ruling was within the court’s discretion. See Fed.R.Evid. 609(b). Considering that there was ample evidence of Hackney’s prior convictions elsewhere in the record,3 the court was within its discretion in prohibiting defense counsel from pursuing Hackney’s criminal record. The probative value of the convictions did not substantially outweigh their prejudicial effect. Fed.R.Evid. 609(b). In addition, defense counsel had not provided the government with “sufficient advance written notice of intent to use such evidence.” Id.
These two instances cited by Buford and Bennie thus fail to support their claim that the district court unduly restricted their cross-examination of Hackney. Other claims of undue restrictions on Hackney’s cross-examination involve only appropriate rulings or mere comments of the district judge in conference. Thus, the district court did not unduly restrict the cross-examination of the government’s key witness.
IV.
Buford and Bennie also contend that their due process rights were denied because the government knowingly used perjured testimony by DEA agent Alter to obtain their convictions. We decline to decide this issue since it is raised for the first time on appeal and no necessary record has been made. Buford and Bennie failed to point out the possible perjury during the trial despite their opportunity to detect the inconsistency in the witness’ testimony. They also neglected to include the issue in their motions for a new trial. Unfortunately for Buford and Bennie, “[i]t is well-established in this court that a litigant cannot present as grounds for reversal an issue not presented to the district court.” United States v. Nero, 733 F.2d 1197, 1207 (7th Cir.1984). This court will, however, consider a claim raised for the first time on appeal when there is “plain error or a defect affecting substantial rights,” United States v. Carreon, 626 F.2d 528, 536 (7th Cir.1980); United States v. Castenada, 555 [831]*831F.2d 605, 610 (7th Cir.), cert. denied, 434 U.S. 847, 98 S.Ct. 152, 54 L.Ed.2d 113 (1977), “if the record is sufficiently developed with respect to such claim,” Nero, 733 F.2d at 1207.
In the case before us, the district court was never requested to determine whether the prosecution knowingly used perjured testimony to obtain the convictions. Counsel for neither of the defendants effectively exposed the testimonial inconsistency in question despite opportunities for cross-examination. See Evans v. United States, 408 F.2d 369, 370 (7th Cir.1969) (“When a criminal defendant, during his trial, has reason to believe that perjured testimony has been employed by the prosecution, he must impeach the testimony at the trial_”). The relevant inconsistency apparently escaped their attention even though Alter’s testimony was very important. We have before us only the briefs and a limited record. These show us only that Alter testified for the government at one point that he did not look under the counter at the Peaks’ store and later that he did look under the counter but did not find a gun or handcuffs.4 Alter’s testimony that he looked under the counter but did not find a gun or handcuffs controverted Buford’s testimony that he loaded a gun, bought handcuffs and put them under the counter to set up his capture attempt. That Alter said he didn’t find these items was damaging to Buford’s defense. It is certainly not clear or even highly probable on the face of the testimony that Alter’s inconsistent remarks constitute perjury. “Perjury is the willful assertion under oath of a false, material fact.” Carey v. Duckworth, 738 F.2d 875, 878 (7th Cir.1984); see also 18 U.S.C. § 1621. “Mere inconsistencies or conflicts [in] the testimony of a witness ... are not enough.” Anderson v. United States, 403 F.2d 451, 454 (7th Cir.1968), cert. denied, 394 U.S. 903, 89 S.Ct. 1009, 22 L.Ed.2d 215 (1969). No inquiries were made as to the reason for Alter’s inconsistent statements. He may have been confused, forgetful or mistaken. The record is devoid of specific evidence that Alter’s second statement, that he looked [832]*832under the counter, was the product of conscious falsification. In the absence of such evidence, we cannot invoke the plain error doctrine to conclude that the prosecution made knowing use of perjured testimony. Thus, the record is insufficient to allow us to find a due process violation at this stage of the proceedings.5
We have found, in the three arguments of Buford and Bennie, no basis for reversing the convictions. Thus, we affirm Buford Peak’s conviction.
V.
We turn now to Bennie’s pro se arguments on his own behalf. Bennie contends that the district court erred in disallowing as hearsay Buford’s testimony about what Bennie said during a telephone conversation with Buford. The district court allowed Buford to relate only his side of the conversation. In rejecting the argument that Bennie’s statements should be admitted under Fed.R.Evid. 803(3), the state-of-mind exception to the hearsay rule, the district judge maintained simply that he was “not going to permit defendants through Mr. Buford Peak to get their stories in the record indirectly.” Transcript at 680. Because we think that Bennie’s statements fall squarely within the state-of-mind exception, we believe it was error to exclude Bennie’s side of the telephone conversation.
A.
Initially, we evaluate Bennie’s offer of proof, the adequacy of which is an essential prerequisite to a finding of error:
Error may not be predicated upon a ruling which admits or excludes evidence unless a substantial right of the party is affected, and ... [i]n case the ruling is one excluding evidence, the substance of the evidence was made known to the court by offer or was apparent from the context within which questions were asked.
Fed.R.Evid. 103(a)(2).
Although Rule 103(a)(2) merely requires the proponent to make the “substance of the evidence” known to the court, an offer of proof generally should state a ground for admissibility, inform the court and opposing counsel what the proponent expected to prove by the excluded evidence and demonstrate the significance of the excluded testimony. Collins v. Wayne Corp., 621 F.2d 777, 781 (5th Cir.1980). This court does not require that a formal offer of proof be made or that the grounds of error be precisely specified. “[I]t is enough if ‘the record shows ... what the substance of the proposed evidence is.’ ” United States v. Sweiss, 814 F.2d 1208, 1211 (7th Cir.1987) (quoting United States v. Alden, 476 F.2d 378, 381 (7th Cir.1973)).
We think that, under the circumstances of this case, Bennie’s counsel made an adequate offer of proof. From the record, we can—though with difficulty—discern the substance of the proposed evidence, its significance to the proponent’s defense and the ground for admissibility.
During direct examination by his counsel, Buford testified that he intended to capture government informant Hackney by luring him to the Peaks’ place of business. He was then asked if he had ever had a conversation with Bennie about his plan. Buford was about to relate the conversation when the government objected that anything Bennie said during the conversation would be hearsay. Bennie’s counsel urged that Bennie’s statements should be admitted under Rule 803(3). The court sustained the government’s objection. Buford then testified as to his side of the conversation in which he told Bennie that he needed a favor, he needed some stalling time, and that he was going to attempt to capture a man.
Following Buford’s testimony, during a court recess, Bennie’s counsel requested to [833]*833make a record about the court's exclusion of Bennie’s responses to Buford over the telephone.
Bennie’s counsel did not request a voir dire of Buford. However, in response to the district court’s comment, “You can make an offer to prove,” Bennie’s counsel offered a brief summary of what Buford would have said on the stand:
It is our understanding—and I would represent to the court—Mr. Buford Peak would testify that he asked Bennie Peak in that conversation to participate in these telephone calls in order to stall these individuals; that he explained generally what was needed; that Bennie Peak was hesitant to do that and was persuaded to do that and that Bennie Peak indicated to the effect that he thought this was the craziest idea he had ever heard or something to that effect. I believe that is substantially what the witness would testify to.
Transcript at 703.
Although the offer of proof is somewhat unclear—it seems to show both Bennie’s intent to go along with the “capture” plan and his doubts about it—it does summarize the substance of the proposed testimony and indicate its importance to Bennie’s defense. This court thus has sufficient information with which to review the district court’s evidentiary ruling.
B.
We examine now the parameters of the state-of-mind exception to the hearsay rule. A statement is hearsay and inadmissible if offered “to prove the truth of the matter asserted.” Fed.R.Evid. 801. It is possible to construe Bennie’s reply to Buford over the telephone as tending to prove the truth of the matter asserted. In any event, the statement was offered to show Bennie’s intent to participate in the “capture” plan and to disprove the intent needed for conviction. Though hearsay, Bennie’s statement that he would go along with the plan can be admitted if it falls within one of the categories of hearsay exceptions. Bennie contends that his statement to Buford should be admitted under Fed.R.Evid. 803(3), the state-of-mind exception.
Rule 803(3) excepts from the hearsay exclusion “[a] statement of the declarant’s then existing state-of-mind, emotion, sensation, or physical condition (such as intent, plan, motive, design, mental feeling, pain and bodily health).” To be admissible, the statement must relate to the declarant’s state of mind as it existed at the time it was uttered and it must satisfy other requirements for admissibility.
Statements indicating state of mind are generally admissible only when state of mind is in issue or when it tends to prove the doing of the act intended. Mutual Life Ins. Co. v. Hillmon, 145 U.S. 285, 12 S.Ct. 909, 36 L.Ed. 706 (1892). Thus, in United States v. Green, 680 F.2d 520, 523 (7th Cir.), cert. denied, 459 U.S. 1072, 103 S.Ct. 493, 74 L.Ed.2d 635 (1982), a kidnapping victim’s statement that the defendant “is still bothering me” was held admissible because it tended to show the victim’s dislike of the defendant and thus that she had been with him against her will.
Similarly, Bennie’s statements to Buford on the telephone reflected his present state of mind when told of the “capture” plan; he thought the idea was “crazy,” but he was willing to cooperate. Bennie offered these statements to show that he lacked the requisite state of mind for conviction. While the government was attempting to show that Bennie had the specific intent to conspire in a drug scheme, Bennie’s reply to Buford on the telephone tends to show that his intent was to help “capture” Hackney. The Second and Eighth Circuits have applied the state-of-mind exception to hearsay statements similar to the ones here. See United States v. Harris, 733 F.2d 994, 1003-05 (2d Cir.1984); United States v. DiMaria, 727 F.2d 265, 270-71 (2d Cir.1984); United States v. Partyka, 561 F.2d 118, 125 (8th Cir.1977), cert. denied, 434 U.S. 1037, 98 S.Ct. 773, 54 L.Ed.2d 785 (1978).
The government makes two arguments, both of which are unpersuasive, in support of the district court’s ruling to exclude the evidence. First, it urges that Rule 803(3) [834]*834only admits bare assertions of state of mind, not details of a conversation. Although it is true that some details accompanying a statement of one’s state of mind may be inadmissible, see United States v. Cohen, 631 F.2d 1223, 1225 (5th Cir.1980), “details” per se are not excluded from the hearsay exception.
Moreover, Bennie merely wanted to admit evidence to show his willingness to join Buford in the “capture” plan and his lack of intent to possess and distribute illegal drugs. It was not his purpose to gain admission into evidence of other details of the conversation. Any significant details could have come in through Buford’s admissible testimony. Bennie’s statement that he would take part in the “capture” plan is a bare assertion of his state of mind, i.e., that he intended to help his brother arrest Hackney. It does not include any inadmissible details.
The government also argues that Bennie’s statement properly was excluded because it was not trustworthy. This argument is based on the impression that Buford was not a credible witness rather than on the degree of reliability inherent in the statement. But the district court, which has broad discretion in evidentiary matters, does not have discretion to exclude testimony because the judge does not believe the witness.6 See DiMaria, 727 F.2d at 272; Fed.R.Evid. art. VIII introductory note on hearsay (quoting Chadbourn, Bentham and the Hearsay Rule—A Benthamic View of Rule 63(4)(c) of the Uniform Rules of Evidence, 75 Harv.L.Rev. 932, 947 (1962)) (“For a judge to exclude evidence because he does not believe it has been described as ‘altogether atypical, extraordinary.’ ”).
Thus, we find that Bennie’s excluded statements fell squarely within the state-of-mind exception to the hearsay rule and that no other grounds support the district court’s ruling to exclude the statements. We therefore hold that it was error to exclude Bennie’s side of the telephone conversation.
C.
An erroneous evidentiary ruling in a criminal ease is reversible error only if it affects a party’s substantial rights. Fed.R. Crim.P. 52(a); Fed.R.Evid. 103(a). The Supreme Court has interpreted this rule to require reversal only if “the error results in actual prejudice because it ‘had substantial and injurious effect or influence in determining the jury’s verdict.’ ” United States v. Lane, 474 U.S. 438, 449, 106 S.Ct. 725, 732, 88 L.Ed.2d 814 (1986) (quoting United States v. Kotteakos, 328 U.S. 750, 776, 66 S.Ct. 1239, 1253, 90 L.Ed. 1557 (1946)); see also United States v. Beasley, 809 F.2d 1273, 1280 (7th Cir.1987).
This court has cautioned against finding an erroneous exclusion of evidence to be harmless:
It is always perilous to speculate on what the effect of evidence improperly excluded would have been. The lay mind evaluates evidence differently from the legal mind, and while many appellate judges have substantial experience with juries and perhaps great insight into the thinking process of juries, others do not. This is a reason to be wary about invoking the doctrine of harmless error with regard to evidentiary rulings in jury cases.
United States v. Cerro, 775 F.2d 908, 915-16 (7th Cir.1985) (citations omitted).
When erroneously excluded evidence would have been the only or primary evidence in support of or in opposition to a claim or defense, its exclusion is deemed to have had a substantial effect on the jury. In Cerro, for example, we suggested that “[i]f the defendant were utterly precluded from defending himself, it would be clear that his conviction had to be reversed even if the evidence of guilt was overwhelming and could not have been offset by the evidence that the defendant would have intro[835]*835duced if allowed to do so.” Id. at 916.7 Moreover, in United States v. Norwood, 798 F.2d 1094, 1098 (7th Cir.), cert. denied, 479 U.S. 1011, 107 S.Ct. 656, 93 L.Ed.2d 711 (1986), although this court held the erroneous exclusion of non-hearsay to be harmless, we implied that had the defendant not been able to present other evidence to support his theory of the case, the error would not have been harmless. Similarly, other courts have held an error not to be harmless when it “ ‘precludes or impairs the presentation of an accused’s sole means of defense.’ ” United States v. Harris, 733 F.2d 994, 1005 (2d Cir.1984) (quoting United States v. Carter, 491 F.2d 625, 630 (5th Cir.1974)).
We find that exclusion of Bennie’s comments to Buford on the telephone substantially influenced the jury. Bennie’s sole defense was that he was helping his brother “capture” the government informant. And the only evidence of that defense was Bennie’s side of the conversation with Buford. This evidence, tending to disprove the intent required for conviction, was vital to Bennie. Without it, he had little chance of acquittal; with it, he could have placed some doubt in jurors’ minds as to his intent. There is a substantial difference between having some evidence and having no evidence to support a defense especially in light of the less than overwhelming evidence against Bennie.8 We, therefore, cannot say with any certainty that the eviden-tiary error had only a slight effect on the jury-
The exclusion of Bennie’s statements substantially impaired his rights in another way. Bennie was denied a jury instruction on the “capture” defense, presumably because he presented insufficient evidence to support it.9 Thus, the jury could not even consider his defense. We will not speculate as to whether the evidence and related instruction would have changed the jury’s verdict.10 It is sufficient that the combined effect of the evidentiary ruling and refused jury instruction clearly had a substantial influence on its determination. The exclusion of Bennie’s comments about his state of mind severely impaired his [836]*836primary defense and led to the refusal of a jury instruction on this defense, thus affecting his substantial rights. The trial court’s evidentiary ruling therefore was reversible error.
VI.
For the reasons stated in parts II, III and IV of this opinion, we affirm Buford Peak’s conviction. We reverse Bennie Peak’s conviction for the reasons given in part V and remand his case to the district court for a new trial. On remand, the district court should admit into evidence Bennie’s state-of-mind responses to Buford during their telephone conversation. In light of this, the court should reevaluate its refusal to give the jury an instruction on Bennie’s theory of defense. Accordingly, the decision of the district court is
AFFIRMED IN PART, REVERSED IN PART AND REMANDED.