WOOD, Circuit Judge.

Norma Leonard-Allen and Walter Stern became entangled in the financial arrangements that underlie this case during the aftermath of a lawsuit in which Stern served as Leonard-Allen's attorney. The government charged that Stern hid some of Leonard-Allen's assets so that she would not have to declare them in her bankruptcy proceeding. It maintained that Stern knew of Leonard-Allen's bankruptcy when he opened certificates of deposit (CDs) with Leonard-Allen's money, and thus that his action amounted to money laundering in violation of 18 U.S.C. § 1956(h). Leonard-Allen, it said, committed perjury in violation of 18 U.S.C. § 1623 when she testified that Stern had not referred her to her bankruptcy lawyer, contrary to her representation on a client-intake form on which she had listed "Walter Stern" as the person who referred her to the bankruptcy lawyer. Both were convicted after a jury trial.

On appeal, Leonard-Allen argues that the client-intake form was subject to attorney-client privilege and should not have been admitted against either defendant. Stern argues that even if the form were not subject to attorney-client privilege, the statement in the form is inadmissible hearsay. He also argues that the court erred when it excluded as hearsay his testimony about why he purchased the CDs and when it excluded as irrelevant testimony from Leonard-Allen's daughters. We affirm Leonard-Allen's conviction because the client-intake form was not a communication made in furtherance of the legal representation and therefore was not subject to the attorney-client privilege. Because the trial court wrongly prevented Stern from testifying about his own conduct—testimony central to Stern's defense that he did not intend to conceal assets— we reverse Stern's conviction.

I

Stern met Leonard-Allen when he represented her in an employment discrimination suit. After the case settled, Stern and Leonard-Allen became romantically involved. They began living together in September 2006, months after Stern opened the first of two CD accounts underlying these charges. Leonard-Allen and her ex-husband had separated in June 2005 and had executed a Marital Settlement Agreement awarding Leonard-Allen $95,000, to be paid in four installments. In July 2005, Leonard-Allen visited a bankruptcy attorney, Mary Losey. In response to a question on Losey's client-intake form asking "How did you select this office?," she checked the box "Friend/Referral" and wrote in Walter Stern's name.

In September 2005, Leonard-Allen filed for bankruptcy, reporting $80,000 in liabilities and only $30,000 in assets. She did not disclose the $95,000 marital settlement. Between June 2005 and January 2006, while her bankruptcy was pending, Leonard-Allen received four personal checks, issued from the divorce attorney's trust account, for a total of $95,000. In January 2006, the bankruptcy court determined that Leonard-Allen had insufficient assets to pay her creditors and discharged her debt. A month later, Leonard-Allen used the proceeds of the first three divorce settlement checks to purchase a teller check; she promptly endorsed that check to Stern. In March 2006, Stern opened a CD account in his name with the proceeds of the check. In August 2006, Leonard-Allen used the proceeds of the fourth divorce settlement check to purchase another teller check, which she also endorsed to Stern. In January 2007, Stern used the proceeds of the second teller check and the first CD to open another CD account in his name. In January 2007, Leonard-Allen's ex-husband's attorney informed the bankruptcy trustee that Leonard-Allen failed to disclose the $95,000 divorce settlement in the bankruptcy proceedings, and in October 2007, the bankruptcy judge revoked the discharge of Leonard-Allen's bankruptcy.

Criminal charges followed, and Leonard-Allen pleaded guilty to two counts of making a false declaration in a bankruptcy proceeding in violation of 18 U.S.C. § 152(3). After doing so, Leonard-Allen was subpoenaed to testify before a grand jury in the case against Stern. She told the grand jury that Stern had not referred her to Losey. The government subpoenaed records from Losey, including the client-intake form where Leonard-Allen had listed "Walter Stern" in the "Friend/Referral" box. Based on that evidence, the government charged Leonard-Allen with making a material false statement in a grand jury proceeding in violation of 18 U.S.C. § 1623. The court admitted the client-intake form as evidence of Leonard-Allen's perjury over Leonard-Allen's objection that it was subject to attorney-client privilege. She was convicted of the offense and sentenced to imprisonment for one year and a day.

Stern was charged with conspiring to commit money laundering in violation of 18 U.S.C. § 1956(h). His defense at trial was that he was unaware of Leonard-Allen's bankruptcy proceeding and therefore did not realize that he was hiding assets when he opened the CDs with Leonard-Allen's money. The court admitted the client-intake form as evidence that Stern likely knew of Leonard-Allen's bankruptcy; it overruled Stern's objection that Leonard-Allen's out-of-court statement on the client-intake form was inadmissible hearsay. See FED.R.EVID. 801 & 802. It reasoned that the form was a business record, admissible under the business-records exception to the hearsay rule, see FED. R.EVID. 803(6)(b). It also held that Leonard-Allen's statement was made in furtherance of a conspiracy between Stern and Leonard-Allen and was thus admissible under the co-conspirator exclusion found in FED. R. EVID. 801(d)(2)(E).

During Stern's testimony, the court prohibited him from answering the following series of questions on the subject of his reason for purchasing the CDs for Leonard-Allen:

The court also excluded testimony that Leonard-Allen's daughters were unaware of Leonard-Allen's bankruptcy. Stern sought to introduce this testimony in support of his claim that he was unaware of the bankruptcy. The court reasoned that the testimony was irrelevant because the daughters had a different relationship with their mother from the one Stern had, and what they knew was therefore not probative of what Stern knew. We first address Leonard-Allen's conviction, then Stern's.

II

Leonard-Allen argues that the intake form was protected by the attorney-client privilege and thus should not have been produced or introduced into evidence at the trial. The scope of attorney-client privilege is a question of law that we review de novo. In re Subpoenaed Grand Jury Witness, 171 F.3d 511, 512 (7th Cir. 1999). The privilege extends to confidential communications between client and attorney, made "in order to obtain legal assistance." Fisher v. United States, 425 U.S. 391, 403, 96 S.Ct. 1569, 48 L.Ed.2d 39 (1976). Its purpose is "to encourage clients to make full disclosure to their attorneys," and its scope is informed by this purpose. Id. Because the privilege may operate "in derogation of the search for truth," we "construe the privilege to apply only where necessary to achieve its purpose." United States v. BDO Seidman, LLP, 492 F.3d 806, 815 (7th Cir.2007) (internal quotation marks and citations omitted). Accordingly, we have said that the privilege covers "only those communications which reflect the lawyer's thinking [or] are made for the purpose of eliciting the lawyer's professional advice or other legal assistance." Id. (internal quotation marks omitted).

Losey's form does not meet that description. Leonard-Allen's disclosure of who referred her does not reflect either the lawyer's or the client's thinking, and it was not instrumental to the substance of the bankruptcy advice that Losey provided. The form is more akin to information about attorneys' fees. The latter information falls outside the scope of the privilege because fees are incidental to the substance of representation. In re Subpoenaed Grand Jury Witness, 171 F.3d at 513 (quoting Matter of Witnesses Before Special March 1980 Grand Jury, 729 F.2d 489, 491 (7th Cir.1984)).

It is true that we have found that the privilege applies in the limited situation when a lawyer's disclosure of the identity of a third party who paid the defendant's fees would implicate another previously unknown client who was involved in the targeted criminal activity. Id. at 514. In that instance, the disclosure of the fee payor risks revealing another client's motive for seeking representation from the lawyer. This risk is not present in Leonard-Allen's acknowledgment that Stern referred her to Losey. That referral sheds no light on Leonard-Allen's motives for seeking legal assistance. On the other hand, her statement on the form was powerful evidence for the government's perjury case, since it contradicted her grand jury testimony.

While the form listed Leonard-Allen's reason for seeking representation as "financial," it was widely known that Losey represented Leonard-Allen for bankruptcy, and so that aspect of the intake form did not reveal otherwise confidential information about Leonard-Allen's motives. If Leonard-Allen had been concerned about the revelation that she had approached Losey for help in financial issues, she might have objected to that portion of the form. It could have been redacted, and the form would have been just as probative in the perjury proceeding. Because the referral statement is incidental to the representation and reveals nothing confidential about Leonard-Allen's motives, it falls outside the scope of the attorney-client privilege, and the district court did not err by admitting it as relevant evidence against both defendants. Furthermore, the statement was one of a party-opponent for Leonard-Allen, and so there was no hearsay bar to its admission. FED.R.EVID. 801(d)(2)(A). We address Stern's additional arguments below.

III

Stern challenges a number of the district court's evidentiary rulings, but we review these decisions only for abuse of discretion. United States v. Gajo, 290 F.3d 922, 926 (7th Cir.2002). We begin with his objection to the court's decision to exclude on hearsay grounds his testimony about why he went to the bank. Hearsay is an out-of-court statement that "a party offers in evidence to prove the truth of the matter asserted in the statement." FED. R.EVID. 801(c). The government contends, and the court ruled, that hearsay responses were called for by the exchange we reproduced above, which included questions about why Stern went to the bank on the day he purchased the CD, whether he planned in advance to purchase the CD, and what he thought was the purpose of his having control over Leonard-Allen's money. This is wrong. We note that the government's lawyer objected so quickly— before Stern could say more than "Well, about three days or so before ..."—that nothing had yet been said that either was or was not hearsay. That was not, however, the basis of Stern's response to the government's objection. Stern's lawyer made the legal argument that even if Stern was planning to repeat something that Leonard-Allen told him about why he should go to the bank and purchase the CDs, that kind of out-of-court statement does not satisfy the definition of hearsay. It does not, because Stern would rot have been introducing any statement of Leonard-Allen's for its truth. A witness's statement is not hearsay if the witness is reporting what he heard someone else tell him for the purpose of explaining what the witness was thinking, at the time or what motivated him to do something. In those circumstances, the out-of-court statement is not being offered as evidence that its contents are true. Talmage v. Hams, 486 F.3d 968, 975 (7th Cir.2007) ("The key issue is ... the effect of the [out-of-court statement] on [the party's] state of mind. The truth or falsity of the [statement] is irrelevant to the latter question, and thus [it] did not fall within the definition of hearsay."); United States v. Hanson, 994 F.2d 403, 406 (7th Cir.1993) ("An. out of court statement that is offered to show its effect on the hearer's state of mind is not hearsay.") (citations omitted). Indeed, the government concedes in its petition for rehearing that "[i]n hindsight, ... the hearsay objections should have been overruled...." Plaintiff-Appellee's Petition for Panel Rehearing Pursuant to Rule 40 of the Federal Rules of Appellate Procedure at 2 n.1.

Because Stern's attorney clearly stated that he was not offering this testimony for its truth, there was no need for any further offer of proof pursuant to Federal Rule of Evidence 103(a)(2). As the excerpt we reproduced shows, the lawyer said that it was "[n]ot for the truth of the matter asserted, Judge. As to impact on him." Just 24 hours earlier, in his opening statement, counsel had asserted that Stern would testify "that Norma became very concerned when she got the $95,000. That she did not want it to be in her care. She wanted to make sure that Mr. Stern could, if possible, hold the money for her so that she wouldn't give it to her children. So she wouldn't have to concern herself that she, being somewhat of a spender, that the money would start to be depleted." The government complains, nonetheless, that counsel should have made a more formal offer of proof in response to the prosecutor's hearsay objection. This is not a case, however, in which counsel remained silent after the objection was made. Instead, counsel stated that the testimony would be limited to showing the impact on Stern. Although the comment was brief, it was enough under the circumstances to "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." United States v. Peak, 856 F.2d 825, 832 (7th Cir.1988). As we said in Peak, and we reiterate here, "[t]his court does not require that a formal offer of proof be made or that the grounds of error be precisely specified. It is enough if the record shows what the substance of the proposed evidence is." Id. (internal quotation marks omitted). Stern's lawyer had no intention of showing that Stern's response would have been limited to his own actions, and so there was no need for any offer of proof along those lines. Instead, as he told the court, he intended to show that Leonard-Allen's out-of-court statements were not hearsay because they would not have been introduced to prove the truth of the matter asserted. As we have already noted, such a use of the statements indeed falls outside the hearsay prohibition.

The court's error was not harmless, because the excluded testimony was central to Stern's defense. Stern maintained that he was unaware of Leonard-Allen's bankruptcy when he purchased the CDs. He intended to support that position before the jury by explaining that Leonard-Allen asked him to hold the money in order to help her manage it. This would have explained how he might have purchased CDs with Leonard-Allen's money without any intent to hide the money from the bankruptcy court (or anyone else). This alternate explanation would have made Stern's defense more believable, because it would have offered the jury a theory under which Stern innocently purchased the CDs, rather than making the purchases to launder Leonard-Allen's divorce proceeds. Since this testimony was central to Stern's defense, we cannot be confident "that the same judgment would have been rendered regardless of the error." Goodman v. Ill. Dep't of Fin. & Prof'l Regulation, 430 F.3d 432, 439 (7th Cir.2005); see also United States v. Peak, 856 F.2d at 834-35.

IV

Because this error calls for reversal, strictly speaking we do not need to determine whether either of the other two evidentiary rulings to which Stern objects—admitting the client-intake form under the co-conspirator exception to the hearsay rule and excluding the testimony of Leonard-Allen's daughters—constituted an abuse of discretion that would warrant reversal. Nonetheless, similar questions may arise if there is a retrial, and so we address them now.

In order for Leonard-Allen's statement on the client-intake form to be admissible under the co-conspirator exception, the government must prove by a preponderance of the evidence that a conspiracy between Leonard-Allen and Stern existed at the time the statement was made, and that the statement was made "during the course and in furtherance of the conspiracy." United States v. Cruz-Rea, 626 F.3d 929, 937 (7th Cir.2010) (citation omitted); United States v. Santiago, 582 F.2d 1128, 1131 (7th Cir.1978), overruled on other grounds by Bourjaily v. United States, 483 U.S. 171, 107 S.Ct. 2775, 97 L.Ed.2d 144 (1987). A timeline of events that the government introduced as an exhibit at trial shows that Leonard-Allen signed the intake form in July 2005, three months before she filed for bankruptcy and seven months before Stern took any action in furtherance of the alleged conspiracy (i.e., opening the first CD). The government's evidence is consistent with the possibility that Leonard-Allen did not even intend to file for bankruptcy at the time she filled out the form, let alone have a plan in place to hide assets from the bankruptcy court. The district court did not identify any supporting evidence when it summarily concluded that "the preponderance of the evidence is that, as charged in the indictment, the money laundering conspiracy existed as of the date, July 6, 2005, when Leonard-Allen completed the intake form." This suggests that the court relied on Leonard-Allen's act of writing Stern's name on the form as the only evidence of a preexisting conspiracy. Standing alone, this statement tells us nothing about the subject matter of any agreement that may have existed between Leonard-Allen and Stern in July 2005. In determining whether the statement is admissible under the co-conspirator exception, the district court should take care to cross the "T's" and dot the "I's": that is, ensure that there is proof of an agreement to launder the money and that Leonard-Allen's act of writing the name fell within the scope of that agreement. We express no further opinion at this juncture on the question whether this evidence will be admissible at the new trial, either under the co-conspirator exception or some other theory. The answer will depend on the evidence before the court in the new trial.

We turn briefly to the testimony of Leonard-Allen's daughters. Evidence is relevant if "it has any tendency to make a fact [of consequence] more or less probable than it would be without the evidence." FED.R.EVID. 401 (emphasis added). The word "any" signals that evidence is relevant even if it only slightly or marginally alters the likelihood of a consequential fact. See Thompson v. City of Chi., 472 F.3d 444, 453 (7th Cir.2006) ("To be relevant, evidence need not conclusively decide the ultimate issue in a case, nor make the proposition appear more probable, but it must in some degree advance the inquiry.") (Internal quotation marks omitted). The fact that the relationship between Leonard-Allen and her daughters is, as the district court observed, "qualitatively different from her relationship with Stern," suggests that what Leonard-Allen's daughters knew is not conclusive proof of what Stern knew. But evidence need not be conclusive proof in order to be admissible, and even if it does not prove that Stern was unaware of the bankruptcy, what Leonard-Allen's daughters knew of the bankruptcy could "in some degree advance the inquiry" into what Stern likely knew, if it suggests that Leonard-Allen was keeping her financial woes to herself.

V

We AFFIRM the conviction of Leonard-Allen. We VACATE Stern's conviction and REMAND for a new trial consistent with this opinion.