WOOD, Chief Judge.

Frank Caira is a smart man who has done some stupid things. Prominent among the latter was his plan for beating a felony drug indictment by having the prosecutor and Drug Enforcement Administration agent on his case murdered. A jury convicted Caira for his role in that plot, and he was sentenced to life plus twenty years. On appeal, he argues that his Fifth Amendment right not to be compelled to testify against himself was violated at trial. He also contends that he was prejudiced by improper jury instructions. We are not persuaded by either argument, and so we affirm the judgment.

I

Caira was an accomplished and well-published medical researcher, but he succumbed to the lure of the illegal drug trade and began producing synthetic drugs, including more than 70,000 pills of MDMA (3, 4-methylenedioxy-N-methylamphetamine), commonly known as ecstasy. DEA Special Agent Patrick Bagley, along with other federal officers, caught wind of Caira's side projects and arrested him; later he was indicted on felony drug charges. After his indictment, Caira met with Assistant United States Attorney Shoshana Gillers (among others) at five proffer sessions to discuss a plea bargain.

On December 21, 2009, Attorney Tamara Holder contacted the Federal Bureau of Investigation with the disturbing information that one of her clients, Ricardo Ruiz, had information about a plot to kill AUSA Gillers and Special Agent Bagley. FBI investigators met with Ruiz, who told them that he had been recruited by a man named Jack Mann to murder Gillers and Bagley in exchange for two kilograms of cocaine and lessons on how to make synthetic drugs. Ruiz provided the agents with copies of court documents from Caira's drug case, as well as an envelope that Mann had given to him. Handwritten notes mentioning Gillers's and Bagley's names appeared on the envelope. Ruiz told the investigators that he had never had any contact with Caira.

On January 13, 2010, the FBI arrested Mann, who also agreed to cooperate. Two days later, Mann met with Caira at a Panera restaurant while wearing a wire. Although the wire malfunctioned and so produced no useful evidence, Caira was arrested as he walked home from the meeting. The agents seized Caira's cell phone, on which they found several text messages between Caira and Mann. Based on the text messages and the testimony of Mann and Ruiz, Caira was indicted on two counts each of conspiracy to commit murder of a United States official in violation of 18 U.S.C. § 1117 and solicitation of a violent felony in violation of 18 U.S.C. § 373.

At trial, the government's case rested primarily on the testimony of Mann and Ruiz and the text messages recovered from Caira's phone. Mann and Ruiz testified that Caira approached Mann about finding a hitman to kill Gillers and Bagley, whereupon Mann recruited Ruiz. In the text messages, Caira and Mann discussed the murder plot in coded language. "When can you get me the paperwork with names of people to be underwritten?" asked Mann at one point. Caira wrote back, "You have two names, and you know the big one," and Mann replied, "Pat is first to be insured." At trial, Caira testified that Mann used the term "underwritten" to "refer[] to contracts in general, and that was a term of having people underwritten to be killed that he came up with." In another text message, Mann told Caira that the plan was a "green light." Asked later what this message meant, Caira said, "He was referring to this whole plan of killing the prosecutor and saying, look, there's a green light[.]"

As these comments reveal, Caira never disputed that a plot to kill Gillers and Bagley existed. Rather, his defense was that the plot was all Mann's idea and that Caira never intended that anyone should be hurt. Caira pointed to cajoling text messages sent by Mann and a threatening voicemail from Ruiz as evidence that Mann and Ruiz were the driving forces behind the plot. For his first witness, Caira attempted to call his former attorney, Jeffrey Fawell, to testify that Caira had shown him Mann's text messages in a panic. This evidence, Caira argued, was relevant to show his state of mind at the time, specifically, that he lacked murderous intent. The government objected that Fawell's testimony would be hearsay, and the district court agreed, stating that "[Fawell's] statement as to what Mr. Caira said without some testimony as to the person making that statement would be rank hearsay.... [T]here are certain conditions precedent which must be met in order to have that evidence come in and not be hearsay." After a short recess, defense counsel announced that Caira would testify, while attempting simultaneously to preserve the Fifth Amendment issue for appeal.

Caira was on the stand for hours. He explained that he met Mann while trying to purchase insurance. Mann and he first discussed Caira's pending drug case as part of a plan calling for Mann to pay a gang leader to turn in other gangsters in exchange for leniency for Caira (the so-called "gang member trade-in"). It was Mann, Caira asserted, not himself, who proposed the idea of killing Gillers and Bagley — a plan that Caira claimed to think was lunacy. He said that he had tried to avoid Mann for months and suggested that Mann and later Ruiz (whom Caira knew only as "Gomez") threatened him. As for the conversation with Fawell, Caira testified:

Caira had nothing more to say about that conversation.

The government's cross-examination of Caira was devastating. It elicited from Caira admissions that he had manufactured drugs for years; sold them for hundreds of thousands of dollars; lied to the IRS, the court, and his wife; and solicited Mann (jokingly, he maintained) to kill one of Caira's lawyer's dogs when the lawyer moved to withdraw from the case. The jury even learned that the dog's name was Jackson. Caira also admitted that the code in Mann's text messages referred to the murder plot. The defense concluded by putting on two more witnesses, including Fawell, who testified about the text-message conversation.

At the conclusion of the defense's case, the parties collaborated on jury instructions. Caira's counsel objected to the inclusion of a list of factors that could corroborate intent, but he did not object to the instructions' discussion of the mental state required to convict. As we noted earlier, the jury found Caira guilty on all counts and he was sentenced to life in prison plus twenty years.

II

Caira's appeal relates only to his conviction. He argues first that the district court's ruling that his testimony was a "condition precedent" to Fawell's testimony violated his Fifth Amendment right against compelled self-incrimination. Second, he argues that the jury instructions failed to explain the mental state required to convict for conspiracy to commit murder and solicitation of murder, and that these erroneous instructions prejudiced his substantial rights. We take up these two arguments in turn.

1. Fifth Amendment

We begin with the question whether the district court erred in ruling that Caira's testimony was a necessary predicate for Fawell's proffered account. Ordinarily, we review the propriety of an evidentiary ruling for an abuse of discretion. United States v. Wilson, 307 F.3d 596, 599 (7th Cir.2002). Caira, however, argues that the district court's ruling violated his Fifth Amendment right to remain silent. To the extent that a person raises a genuine constitutional claim, our review is de novo, but if the litigant has simply dressed an evidentiary ruling in constitutional clothing, we continue to use the abuse-of-discretion standard. As we explain below, Caira's arguments do not trigger more than deferential review. Id.

Under the Federal Rules of Evidence, hearsay is defined as "a statement that: (1) the declarant does not make while testifying at the current trial or hearing; and (2) a party offers in evidence to prove the truth of the matter asserted in the statement." FED.R.EVID. 801(c). The statements at issue here were made during a conversation between Fawell and Caira, and they were about text messages that Caira had received from Mann. In those statements, Caira supposedly told Fawell that he had received Mann's messages; Fawell then advised him to stay away from Mann. Neither Caira nor Fawell made his statements "while testifying at the current trial," and so the first part of Rule 801(c)'s definition was met. The question is whether any of the contested statements was offered for the truth, or if instead it was offered for another purpose. In our view, the more natural interpretation is that these statements were offered to show Caira's state of mind, not to prove the point that he actually had received text messages from Mann or that he should avoid Mann. Because the statements were not offered to prove the truth of the matter asserted, the district court erred by characterizing them as hearsay.

That conclusion in itself, however, does not compel a ruling in Caira's favor. He urges that this evidentiary error had the effect of forcing him to take the stand, and further that this compelled testimony necessarily violated his rights under the Fifth Amendment. But the link between an evidentiary error and a constitutional violation cannot be drawn so readily. As we noted in United States v. Paladino, 401 F.3d 471 (7th Cir.2005), the Supreme Court has held that there is no compulsion as the Fifth Amendment uses that concept in this situation, because the defendant retains the option of standing on his right not to testify and seeking appellate correction of the evidentiary ruling. Id. at 477, citing Luce v. United States, 469 U.S. 38, 41-43, 105 S.Ct. 460, 83 L.Ed.2d 443 (1984).

Caira asks us to overrule Paladino on the ground that it unjustifiably extends the Supreme Court's reasoning in Luce, a case in which the defendant did not testify at trial. In contrast, in both Paladino and the present case, the defendant did testify. Caira is correct that Luce addresses the situation in which the defendant elects not to testify in light of the trial court's (erroneous) preliminary determination that the government would be permitted to introduce certain impeachment evidence. See Luce, 469 U.S. at 43, 105 S.Ct. 460 ("We hold that to raise and preserve for review the claim of improper impeachment with a prior conviction, a defendant must testify."). The question is whether we were correct in Paladino to apply the Luce principle (reaffirmed in Ohler v. United States, 529 U.S. 753, 759, 120 S.Ct. 1851, 146 L.Ed.2d 826 (2000)) to cases in which the defendant does testify in response to an evidentiary error by the district court. We are satisfied that the answer is yes.

As we noted in Paladino, "there is no compulsion in such a case, since the defendant has the option of refusing to testify and instead, if he is convicted, of obtaining appellate correction of the erroneous evidentiary ruling and with it a new trial." 401 F.3d at 477. We acknowledged that "this rule puts the defendant to a hard tactical choice," but we were concerned that "the alternative would be to give him two bites at the apple: testify, and try to win an acquittal; if that fails, appeal and get a new trial on the basis of the judge's ruling." Id.; see also Wilson, 307 F.3d at 599-600 (rejecting defendant's argument that such a choice impermissibly puts defendant "on the horns of a dilemma"). We see no reason to jettison that logic. Cf. McGautha v. California, 402 U.S. 183, 217, 91 S.Ct. 1454, 28 L.Ed.2d 711 (1971) (concluding that "the policies of the privilege against compelled self-incrimination are not offended when a defendant in a capital case yields to the pressure to testify on the issue of punishment at the risk of damaging his case on guilt").

As in Luce and Paladino, the district court's decision here left the defendant with a difficult choice, but a choice nonetheless. Caira's decision was voluntary, strategic and fully informed — that is, it was the antithesis of compulsory. Had the jury believed him, he might be a free man today. But it did not. We are satisfied that Caira's decision to testify was based on much more than the district court's evidentiary ruling. That is not unusual: "an accused's decision whether to testify `seldom turns on the resolution of one factor[.]'" Luce, 469 U.S. at 42, 105 S.Ct. 460 (quoting New Jersey v. Portash, 440 U.S. 450, 467, 99 S.Ct. 1292, 59 L.Ed.2d 501 (1979) (Blackmun, J., dissenting)).

Understood as an ordinary evidentiary error, the mistaken decision to exclude Fawell's testimony would not call for reversal unless it affected Caira's substantial rights. See FED. R. CRIM. P. 52(a). It did not have such an effect. First, the proffered testimony concerned only a small part of Caira's overall defense. Weighed against the incriminating text messages, the fact that the targets of the alleged plot were the prosecutor and DEA agent involved in Caira's own case, and the testimony of Mann and Ruiz, Fawell's testimony would not have been likely to influence the jury's verdict. In addition, Caira elected to testify before offering his other witnesses. Cf. Brooks v. Tennessee, 406 U.S. 605, 610-11, 92 S.Ct. 1891, 32 L.Ed.2d 358 (1972) (striking down state statute requiring defendant to testify first or not at all because the rule prevented defendant from assessing the necessity of his testimony). When Caira took the stand, his testimony touched only briefly on the conversation with Fawell and went into much greater detail about his interactions with Mann. Caira explains this by saying that once he decided to take the stand, he had to testify about more than the conversation with Fawell or else the jury would have wondered why he did not address the rest of the government's case. But the fact remains that Caira used his opportunity to testify to bolster his side of the story before the jury. In the end, Caira cannot show that the mistaken exclusion of one line of evidence had the necessary effect on his rights.

Our conclusion is bolstered by the fact that if Fawell's testimony were really so vital to his case, Caira could have directly challenged its exclusion on appeal. Wrongful exclusion of material evidence can, in some circumstances, amount to a Fifth Amendment violation if it deprives the defendant of due process. This is a distinct problem from the one raised by compulsory self-incrimination. We do not have before us a case in which the defendant's only exculpatory evidence other than his own testimony is wrongfully excluded by the district court, and so we express no opinion about that situation. We hold only that because Caira's decision to testify was voluntary, under the governing Supreme Court cases there is no merit to his argument that his testimony was compelled in violation of the Fifth Amendment privilege against self-incrimination. Moreover, the evidentiary error we have identified did not affect his substantial rights.

2. Jury Instructions

Caira's second argument is that he was prejudiced by jury instructions that failed to explain the required mental states. But at trial Caira did not raise the challenges that he now makes. Our review is therefore only for plain error. FED.R.CRIM.P. 30(d), 52(b); see also United States v. Jackson, 479 F.3d 485, 491 (7th Cir.2007). As the Supreme Court explained in Puckett v. United States, 556 U.S. 129, 129 S.Ct. 1423, 173 L.Ed.2d 266 (2009), plain-error review proceeds in four steps:

556 U.S. at 135, 129 S.Ct. 1423 (internal citations omitted; emphasis in original). Applying this test, which originated in United States v. Olano, 507 U.S. 725, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993), we have observed that "it is rare that we reverse a conviction on the basis of an improper jury instruction to which there was no objection." United States v. Wheeler, 540 F.3d 683, 689 (7th Cir.2008); see also United States v. Griffin, 84 F.3d 912, 925 (7th Cir.1996) ("Our plain error review is particularly light-handed in the context of jury instructions.").

Caira's complaints focus on the court's instructions on solicitation and conspiracy. We look first at the solicitation instruction, which was as follows:

We find no plain error in this instruction. In order to meet its burden of proof on the solicitation charge, the government was required to establish (1) strongly corroborative circumstances that Caira intended to arrange the murders and (2) that Caira solicited, commanded, induced, or otherwise tried to persuade another person to carry out the crime. 18 U.S.C. § 373; United States v. Hale, 448 F.3d 971, 982 (7th Cir.2006). The instruction we have reproduced adequately conveys those statutory requirements. It informs the jury that it must find that the defendant "intended" that another person engage in conduct constituting a violent felony. It stresses that the "surrounding circumstances in general must indicate that the defendant was serious when he solicited the criminal conduct." The court was not required to include murder-specific terms such as "premeditated" and "malice aforethought" — indeed, because the crime charged was solicitation of violent crime, the inclusion of such terms would have been unnecessary and distracting. See United States v. Hill, 252 F.3d 919, 923 (7th Cir.2001) ("Unless it is necessary to give an instruction, it is necessary not to give it, so that the important instructions stand out and are remembered.").

The conspiracy instruction requires more discussion. On conspiracy, the court had this to say:

The alleged conspiracy was the plot to murder AUSA Gillers and Special Agent Bagley. This is important, because "in order to sustain a judgment of conviction on a charge of conspiracy to violate a federal statute, the [g]overnment must prove at least the degree of criminal intent necessary for the substantive offense itself." United States v. Feola, 420 U.S. 671, 686, 95 S.Ct. 1255, 43 L.Ed.2d 541 (1975). Yet the court never told the jury that it had to find that Caira had the necessary state of mind for a murder conviction — premeditation and malice aforethought. See United States v. Brown, 518 F.2d 821, 825-26 (7th Cir.1975). On the other hand, the instruction tracked Instruction 5.08(A) of the 2012 pattern criminal jury instructions, which endeavor to keep instructions as simple as possible, while covering all essential points.

But instructional error alone is not enough to support reversal. Even if either this instruction or the general failure of the instructions to tell the jurors that a conspiracy to murder exists only if the conspirators acted with the prescribed mental state was erroneous, Caira must also show that the error prejudiced his substantial rights and "seriously affects the fairness, integrity, or public reputation of judicial proceedings." Olano, 507 U.S. at 736, 113 S.Ct. 1770. This is a heavy burden.

When a defendant contends that an instruction was deficient, the key question is the effect of the error. United States v. Kerley, 838 F.2d 932, 938 (7th Cir.1988). A jury charge that fails properly to describe an element of the crime is not always considered reversible error. See Neder v. United States, 527 U.S. 1, 8-10, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (holding that instructional error is subject to harmless-error review); Pope v. Illinois, 481 U.S. 497, 502-04, 107 S.Ct. 1918, 95 L.Ed.2d 439 (1987). In Neder, the Court held that the verdict could stand in the face of an instruction that omitted an element of the crime if it appeared "beyond a reasonable doubt that the error complained of did not contribute to the verdict obtained." 527 U.S. at 15, 119 S.Ct. 1827, citing Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). That is the test we will apply to Caira's conviction.

The jury was told that it needed to find a conspiracy, which the instructions defined as "an agreement between two or more persons to accomplish an unlawful purpose." There was ample evidence to permit it to find that the plot to kill ADA Gillers and Agent Bagley met that definition. In finding that Caira "knowingly became a member of the conspiracy with an intention to further the conspiracy," the jury necessarily had to find that Caira joined the conspiracy with an intention to further the plan to kill Gillers and Bagley. The testimony from Mann and Ruiz, coupled with Caira's text messages, provide strong support for the finding that Caira joined the conspiracy knowing its object and intending it to succeed.

Especially under plain-error review, we must assess the effect of any instructional error against the backdrop of the entire trial. Here, Caira's intent was the main focus for both parties. As his own appellate brief indicates, "closing arguments [made] clear that Caira's mental state was the primary point of contention." Caira argues that a "juror who read the text messages could easily have thought ... that [Caira] had some degree of nebulous interest that might constitute `agreement'" without realizing that the government needed to show that Caira "manifest[ed] the heightened mental state of malice aforethought and premeditation." But Caira's having a "nebulous interest" was not a version of events presented to the jury. Rather, the jury heard two distinct storylines: one in which Caira coordinated hits against Gillers and Bagley, and one in which the plot was all Mann and Ruiz's. The jury knew exactly what it was being asked to decide; it simply did not buy Caira's story.

Even if error in the instructions prejudiced Caira's substantial rights, we would not reverse unless "the error seriously affects the fairness, integrity, or public reputation of judicial proceedings." Olano, 507 U.S. at 736-37, 113 S.Ct. 1770. It did not. Caira's own testimony undermines his argument that he never meant to have any murders committed. For example, this exchange occurred during Caira's cross-examination:

If that were not enough, there was also this exchange: Q: Who is they?

In light of these incriminating admissions, even if the erroneous instruction prejudiced Caira, the conviction does not seriously affect the fairness, integrity, or public reputation of judicial proceedings. We therefore AFFIRM the judgment of the district court.