AMBRO, Circuit Judge

Douglas A. Campbell (Argued), Kathryn L. Harrison, Campbell & Levine, 310 Grant Street, 1700 Grant Building, Pittsburgh, PA 15219, Counsel for Appellants/Cross-Appellees

Neal H. Levin (Argued), Freeborn & Peters, 311 South Wacker Drive, Suite 3000, Chicago, IL 60606, Counsel for Appellee/Cross-Appellant

Before: AMBRO, SHWARTZ, and FUENTES, Circuit Judges

OPINION OF THE COURT

AMBRO, Circuit Judge

When his old law firm broke its lease, attorney Paul Titus was on the hook for millions of dollars in unpaid commercial rent. The landlord tried to recover the rent by targeting the wages Mr. Titus was earning at his new firm. But Mr. Titus’s wages never passed through his hands alone; instead, they were deposited by his new firm directly into a bank account owned by both Mr. Titus and his wife as tenants by the entireties.

Eventually, Mr. Titus was forced into bankruptcy and the landlord’s claim became a claim of the bankruptcy trustee. Now, after two trials in the Bankruptcy Court and two appeals to the District Court, we reach three conclusions. First, Mr. and Mrs. Titus are liable for a fraudulent transfer. When the wages of an insolvent spouse are deposited into a couple’s entireties account, both spouses are fraudulent transferees. Second, as for the precise measure of the Tituses’ liability, the bankruptcy trustee waived any challenge to the method used by previous courts to calculate fraudulent-transfer liability. Going forward, however, we clarify how future courts should measure liability when faced with an entireties account like the Tituses’ — an account into which deposits consist of both (fraudulent) wages and (non-fraudulent) other sources, and from which cash is spent on both (permissible) household necessities and (impermissible) other expenditures. Until now, a trustee somehow had to show that wage deposits were impermissibly spent on non-necessary expenditures, even though wage and nonwage deposits had become commingled in the account. Rather than expect a trustee to trace the untraceable, future courts should generally presume that wage deposits were spent on non-necessary expenditures in proportion to the overall share of wages in the account as a whole. Third, in evaluating the Bankruptcy Court’s application of the method in play at the time of its decision, we perceive no clear error. Thus we affirm.

I. Background

A. Facts

In 1999, the Pittsburgh law firm of Titus & McConomy dissolved. One of the firm’s named partners, Paul Titus, joined another firm, Schnader Harrison Segal & Lewis LLP. The Schnader firm began depositing Mr. Titus’s wages into a bank account he owned jointly with his wife.

Evidently the dissolved Titus firm had walked away from its commercial lease. To recover rent that had gone unpaid since the dissolution, the landlord brought a breach-of-contract suit against the former partners of the Titus firm and ultimately secured a multimillion dollar judgment against the partners, including Mr. Titus.

Armed with the breach-of-contract judgment, the landlord set its sights on the wages that Mr. Titus’s new employer, the Schnader firm, was depositing into the Tituses’ bank account. It brought a fraudulent-transfer action in Pennsylvania state court against Mr. and Mrs. Titus. This triggered an involuntary bankruptcy against Mr. Titus. Thus the landlord’s fraudulent-transfer claim became a claim of the bankruptcy trustee in the Bankruptcy Court. B. Procedural History in Bankruptcy

After a first trial, the Bankruptcy Court concluded that the direct deposit of wages into the Tituses’ bank account was a fraudulent transfer that the trustee could recover from either Mr. or Mrs. Titus, who jointly owned the account as tenants by the entireties. As for the measure of liability, Mr. and Mrs. Titus were liable for the amount of Mr. Titus’s wages that were "not spent on necessities." In re Titus (Titus I ), 467 B.R. 592, 620 (Bankr. W.D. Pa. 2012).

On appeal, the District Court affirmed that the wage deposits were a fraudulent transfer. It remanded for a new trial, however, to give the Tituses a second chance to identify both the source of certain "unexplained deposits" into the bank account and the destination of certain "unknown expenditures" from the account. Titus v. Shearer (Titus II ), 498 B.R. 508, 520, 525 (W.D. Pa. 2013).

After a second trial, the Bankruptcy Court made the following findings as to deposits into, and expenditures from, the bank account:

See In re Titus (Titus III ), 566 B.R. 755, 797 (Bankr. W.D. Pa. 2017). A note on terminology: The Bankruptcy Court divided the spending from the account into "necessity expenditures" and "non-necessity expenditures," which it sometimes called "Non-Objectionable Expenditures" and "Objectionable Expenditures," respectively. See, e.g. , id. ; see also id. at 765, 768, 777–78. For simplicity, we use the necessity/non-necessity nomenclature. To give some content to these terms, "necessities" included items such as a lawnmower and batteries, id. at 792–93, while the Tituses’ "non-necessities" included, among other things, their grandson’s application fee to Notre Dame, id. at 797.

Using the figures set out above, the Bankruptcy Court went about calculating the Tituses’ liability. But the Court immediately hit a roadblock: Because money is fungible and wage and nonwage deposits commingled in the account, it was impossible to determine whether a dollar of wages was eventually spent on a permissible "necessity" or an impermissible "non-necessity." As a result, the Court had to calculate liability indirectly.

It did so using what it could measure: nonwage deposits and non-necessity spending, which are represented below the dotted line in the chart. The Court’s underlying assumption was that all explained, nonwage sources of cash in the account (both explained nonwage deposits and cash already in the account) were spent on non-necessities before any wage deposits were impermissibly spent on whatever non-necessities remained. Thus the Tituses’ total liability was:

(Non-Necessities) – (Explained Nonwages) – (Initial Balance)

= $1,000,133.51 – $634,998.83 – $91,272.00

= $273,862.68.

Id. at 799. Over the Tituses’ objection, the Court did not offset their non-necessity spending even further by the amount of unexplained nonwage deposits. Had it done so, an additional $268,167.09 would have been shaved off the remaining non-necessity spending, leaving a judgment against the Tituses of only $5,695.59.

The District Court affirmed. Neither side is fully satisfied with various rulings of the Bankruptcy and District Courts, and both have appealed.

II. Jurisdiction and Standard of Review

The District Court had jurisdiction to review the final order of the Bankruptcy Court under 28 U.S.C. § 158(a). We have jurisdiction to review the final order of the District Court per 28 U.S.C. § 158(d) and 28 U.S.C. § 1291. Because the District Court acted as an appellate court, we review its determinations de novo . In re Bocchino , 794 F.3d 376, 379 (3d Cir. 2015). We review the legal conclusions of the Bankruptcy Court de novo and its factual determinations for clear error. Id. at 380.

III. Discussion

After two trials in the Bankruptcy Court, two appeals to the District Court, and four rounds of briefing in our Court, there are three issues for our review:

(1) Are the Tituses liable for a fraudulent transfer?

(2) Did the trustee waive any challenge to the method used to calculate the Tituses’ liability?

(3) Did the Bankruptcy Court clearly err in applying the method it used?

We include an additional area of discussion on the second issue. Even if the trustee waived its challenge to the calculation method, should future courts measure liability for commingled accounts differently?

A. Threshold Fraudulent-Transfer Liability

The bankruptcy trustee "may avoid any transfer of an interest of the debtor in property" if the transfer "is voidable under applicable law by a creditor." 11 U.S.C. § 544(b)(1). The applicable law here, the Pennsylvania Uniform Fraudulent Transfer Act (PUFTA), permits a creditor to avoid a fraudulent transfer "to the extent necessary to satisfy the creditor’s claim." 12 Pa. Cons. Stat. § 5107(a)(1).

We reach three conclusions on the threshold question of the Tituses’ fraudulent-transfer liability. First, the wage deposits into the Tituses’ entireties account were a "transfer" under the PUFTA. Second, Mrs. Titus is personally subject to PUFTA liability as an entireties tenant. Third, Mr. Titus is subject to transferee liability even though he is the debtor-transferor as well. As a result, the wage deposits constituted a fraudulent transfer that the bankruptcy trustee could avoid.

1. The wage deposits constituted a "transfer."

"[T]he direct deposit of wages into an entireties account is a ‘transfer’ of an ‘asset’ under the PUFTA." Wettach , 811 F.3d at 115. This statement settles the question whether the wage deposits from the Schnader firm into the Tituses’ entireties account were a transfer.

The reasoning behind this conclusion is as follows. On a macro level, Mr. Titus’s wages (i) began as his "asset" for purposes of the PUFTA and (ii) were not his "asset" once they were in the entireties account. Id at 114–15. That change in status is deemed a "transfer." Id. at 115.

As to the first point, Mr. Titus "exercised control over where his employer deposited his wages." See id. at 114. This control overrode Pennsylvania’s baseline rule that "wages" are exempt from creditors "while in the hands of the employer." 42 Pa. Cons. Stat. § 8127(a). In other words, when the Schnader firm "initiated the direct deposit," the wages left Schnader’s "hands" and became, temporarily, an asset of Mr. Titus. See Wettach , 811 F.3d at 114–15.

As to the second point, the wages ceased being an "asset" of Mr. Titus once they were in the entireties account. The definition of "asset" under the PUFTA excludes property held in a tenancy by the entireties "to the extent it is not subject to process by a creditor holding a claim against only one tenant." 12 Pa. Cons. Stat. § 5101(b). That predicate is satisfied here: The landlord held a claim against only one entireties tenant (Mr. Titus), and "entireties property is unavailable to satisfy the claims of the creditor of only one of the tenants." Garden State Standardbred Sales Co. v. Seese , 417 Pa.Super. 15, 611 A.2d 1239, 1243 (1992). As a result, once the wage deposits reached the entireties bank account, they were no longer an "asset" of Mr. Titus under the PUFTA.

Putting these points together, Mr. Titus started with an "asset" and later relinquished it to the entireties account. This maneuver meets the PUFTA’s definition of "transfer" as an "indirect ... disposing of or parting with an asset or an interest in an asset." 12 Pa. Cons. Stat. § 5101(b). To sum up, Mr. Titus, "by depositing [his] own funds into an entireties bank account, is converting [the] funds into entireties property and, thereby, transferring [that] property for purposes of the [PUFTA]." See In re Meinen , 232 B.R. 827, 841 (Bankr. W.D. Pa. 1999) (setting out the reasoning above).

2. Mrs. Titus is a transferee subject to PUFTA liability.

Even assuming that the wage deposits were a "transfer" under the PUFTA, Mrs. Titus has a further objection of her own — that her status as a co-tenant by the entireties cannot open her up to personal liability for wages deposited by her insolvent husband into their joint account.

Case law prevents this position’s success. "[W]hen a spouse conveys individual property to a tenancy by the entireties in fraud of creditors, the creditor may nevertheless execute against the property so conveyed." Garden State , 611 A.2d at 1243 ; see also Stinner v. Stinner , 300 Pa.Super. 351, 446 A.2d 651, 652 (1982) (same). Numerous courts have applied this rule to hold an insolvent debtor’s spouse personally liable for a fraudulent transfer. See, e.g. , Wettach , 811 F.3d at 114–15 ; Meinen , 232 B.R. at 840–41 ; Garden State , 611 A.2d at 1243 ; Stinner , 446 A.2d at 652.

In doing so, courts have acknowledged the point that Mrs. Titus urges here — that this liability rule leads to a harsh result. See, e.g. , Stinner , 446 A.2d at 654–55 (McEwen, J., concurring) (applying the rule "even though I find it most difficult to accept the determination that the regular routine deposit of salary and bonuses by a husband, into a household checking account owned by himself and his wife as tenants by the entireties, is a conveyance of individual property in fraud of creditors"). One court even "invite[d] the General Assembly" to scrap the usual creditor-friendly presumption of a fraudulent transfer "when the conveyance results in the creation of entireties property." Garden State , 611 A.2d at 1243–44. All courts nonetheless continue to apply the rule.

3. Mr. Titus is subject to PUFTA transferee liability even though he is the debtor-transferor as well.

Mr. Titus is both transferor and transferee. As an individual debtor-transferor, he is subject to liability under the landlord’s claim for breach of the lease agreement. As a transferee, he has fraudulent-transfer liability as a tenant of the entireties account. In sum, his different capacities make him liable in different ways. His argument that he cannot be both transferor and transferee therefore fails.

Nor is there a risk of double recovery — that is, one recovery from Mr. Titus as an individual debtor and another from him as an entireties tenant. Once the trustee secures a recovery from one source, he will not have recourse against the other source. Cf. In re Integra Realty Res., Inc. , 354 F.3d 1246, 1266 (10th Cir. 2004) (noting that the trustee may only "restore the estate to the financial condition it would have enjoyed if the transfer had not occurred") (quotations omitted). The fraudulent-transfer suit was only instituted as part of the overall collection effort to satisfy the judgment entered on the breach of the lease agreement.

B. Method for Calculating PUFTA Liability

Having concluded that Mr. and Mrs. Titus can be individually liable for a fraudulent transfer of Mr. Titus’s wages, we reach the question of how to measure that liability. We begin with the baseline rule that a transfer is not "fraudulent" under the PUFTA if the wages deposited into the entireties account are "used to pay for reasonable and necessary household expenses." Wettach , 811 F.3d at 105 (quotations omitted) (discussing 12 Pa. Cons. Stat. § 5104(a)(2) ); see also 11 U.S.C. § 550(a) (providing that the trustee in a § 544 action "may recover" from a transferee either "the property transferred" or "the value of such property," but not explaining how to identify the property or calculate its value in the first place). This rule accounts for the Bankruptcy Court’s decision, explained above, to segregate expenditures from the account into "necessities" and "non-necessities." But, having determined the amounts of wage deposits, nonwage deposits, necessity spending, and non-necessity spending, the question remains how to combine these inputs to reach a figure for the Tituses’ liability. This question, in turn, depends on the allocation of burdens in a fraudulent-transfer action in Pennsylvania.

Between the two trials in this case, we clarified the burdens in a PUFTA action. First, our Court presumes that "funds deposited into an entireties account were not in exchange for reasonably equivalent value." Wettach , 811 F.3d at 111. In our case, this means we presume that the wages in question were not spent on necessities. See id. Second, the Tituses may rebut that presumption by producing "some evidence as to uses of funds in the entireties account." Id. at 109 (quotations omitted). Imposing this burden of production on the Tituses "serves an information-forcing purpose" by requiring them "to come forward with information" about "how they used funds transferred into [the] entireties account." Id. Third, once the Tituses have met their burden of production, the trustee bears the burden of persuasion "as to all elements of a constructive fraudulent-transfer claim under the PUFTA." Id. at 107. Among other things, the trustee must prove by a preponderance of the evidence that wage deposits were not spent on necessities.

But the trustee is faced with what appears to be an impossible task in a commingled account, circumstances that did not exist in other cases before us. Because money is fungible, and funds from multiple sources commingle in the entireties account, "it may be impossible to determine what deposit was used for a particular expenditure." In re Wettach , 489 B.R. 496, 507 (Bankr. W.D. Pa. 2013) ; see also Oberdick , 490 B.R. at 710 n.15 (describing the "impossible burden" on the trustee to trace deposits into the account to spending from the account).

No wonder, then, that the trustee here could not carry his burden of persuasion. For example, in the first trial in this case, the Bankruptcy Court explained that it was "at least as likely as not" that a given dollar of deposits went toward necessity spending as toward non-necessity spending. Titus I , 467 B.R. at 624. As a result, the trustee "ha[d] not preponderantly proven" that wages were improperly spent on non-necessities. Id. The uncertainty of the dollar’s final destination, moreover, is compounded by a "fairness issue" — namely, Mr. and Mrs. Titus "created the uncertainty by commingling the funds," but the trustee "is expected to somehow unravel it." See Oberdick , 490 B.R. at 710 n.15.

Faced with this commingling problem, every court to encounter the issue has adopted a baseline assumption: All explained nonwage deposits were spent on non-necessities before any wage deposits were spent on non-necessities. E.g. , Titus v. Shearer (Titus IV ), No. AP 10-2338, 2017 WL 5467712, at *5 (W.D. Pa. Nov. 14, 2017) ("The bankruptcy court found ... that all non-necessities were purchased with explained nonwages."). Another way of stating the same assumption is that all wage deposits were spent on necessities before being spent on anything else. Either phrasing expresses the same idea: Deposited funds travel horizontally, rather than diagonally, across the charts reproduced in this opinion. See supra p. 298; infra p. 303. The assumption has supported a method for calculating PUFTA liability, which parties and courts have dubbed the "Non-Necessities Approach" or the "Other Deposit Methodology." It provides the following formula for calculating fraudulent-transfer liability:

Liability = (Non-Necessity Spending) – (Nonwage Deposits) .

In this case, the trustee waived any challenge to the selection of this method and formula. An issue is waived on remand if it was "not raised in a party’s prior appeal." Skretvedt v. E.I. DuPont De Nemours , 372 F.3d 193, 203 (3d Cir. 2004). Also, "when a party fails to raise an issue in the bankruptcy court, the issue is waived." In re Kaiser Grp. Int’l Inc. , 399 F.3d 558, 565 (3d Cir. 2005). The trustee here did not object to the Non-Necessities Approach during the first trial in the Bankruptcy Court or in the first appeal to the District Court. Instead, he waited to challenge it for the first time on remand to the Bankruptcy Court for a second trial. See Titus III , 566 B.R. at 769. Thus the Bankruptcy Court and District Court agreed that the choice of method had been waived. See, e.g. , id. at 773. We affirm that conclusion. Hence we turn to its application in the next section.

Before doing so, however, we set out a different way to calculate liability for future courts facing commingled funds: the pro rata approach. Under this approach, we presume, absent other evidence, that spending out of the entireties account was made up of a mixture of wage and nonwage deposits in proportion to the overall ratio of wage to nonwage deposits in the account. As we explain below, this approach addresses practically the commingling of fungible funds in the account and is not foreclosed by precedent in our Circuit.

1. The pro rata approach accounts practically for the commingling of fungible funds.

As noted, the first Bankruptcy Court in this case stated that it was "at least as likely as not" that a dollar of nonwage deposits funded non-necessity spending, and that the trustee had therefore failed to prove by a preponderance of the evidence that wage deposits impermissibly funded non-necessities. See Titus I , 467 B.R. at 624. This is incorrect. Absent unusual circumstances, a dollar deposited into the account is equally likely to be spent on necessities and on non-necessities only if the same amount is spent on both necessities and non-necessities . In all other situations, the deposited dollar is more likely to be spent on whichever category of spending (necessities or non-necessities) is larger. By the same token, a dollar spent from the account is more likely to come from whichever category of deposits (wage or nonwage) is larger.

The pro rata approach accounts for the fungibility of wage and nonwage funds that are commingled in the entireties account. In our case, the liability would be calculated based on the inflows and outflows found by the second Bankruptcy Court decision (for simplicity, and to be consistent with our conclusion in the next section, we have eliminated "unexplained" nonwage deposits):

Titus III , 566 B.R. at 797. The total amount of money flowing into the account is the sum of wage deposits, nonwage deposits, and preexisting cash in the account:

Total Inflows = (Wages) + (Nonwages) + (Preexisting Cash)

= ($1,125,255.58) + ($634,998.83) + ($91,272)

= $1,851,526.41.

Thus the calculation of wage deposits as a percentage of total inflows is:

(Wage Deposits) / (Total Inflows)

= ($1,125,255.58) / ($1,851,526.41)

= 60.8%.

Hence we can presume that, of the $1,000,133.51 spent on non-necessities, 60.8% impermissibly came from wage deposits. The Tituses’ liability would be that wage-derived portion:

(0.608) * ($1,000,133.51) = $607,825.96.

Eyeballing these figures, we note that this measure of liability makes intuitive sense: Wages account for just under two-thirds of all deposits into the account, so it stands to reason that just under two-thirds of all non-necessity spending came from wage deposits. Appropriately, then, the Tituses’ liability under the pro rata approach would be just under two-thirds of all non-necessity spending.

We add one further note on the mechanics of the pro rata approach. We alluded earlier to "unusual circumstances" that could overcome the default presumption that spending out of the entireties account is made up of a mixture of wage and nonwage dollars in proportion to the overall ratio of wage to nonwage deposits into the account. See supra p. 303. Recall that the pro rata approach rests on our observation that a trustee should not be asked to trace the untraceable. It follows that the presumption would yield where a factfinder could trace the (ordinarily) untraceable — in other words, where the factfinder could track a dollar from a given category of deposits into a given category of spending.

Say, for instance, that a trial court could trace X dollars of nonwage deposits into an account to X dollars of non-necessity spending from the account. (An example might be monies placed into the account from a bequest requiring its spending on what is not necessary.) Before performing the pro rata calculation for the rest of the cash inflows and outflows, the trial court would reduce both its nonwage deposit figure and its non-necessity spending figure by X . The result of this reduction in nonwage deposits (while wage deposits remain constant) would be a greater percentage share of all deposits into the account coming from wages. This greater percentage share would then be applied to the reduced amount of total non-necessity spending.

In sum, the trial court should trace whatever is traceable before using the pro rata approach to proportionally derive the untraceable flows. We leave to the trial court’s discretion the threshold decision whether it is able to trace the ordinarily untraceable.

2. The pro rata approach is not foreclosed by precedent in our Circuit.

The only possible precedent of this Court, Wettach , 811 F.3d 99, does not foreclose the pro rata approach. In the course of setting out the rebuttable presumption and the burdens of production and persuasion, the Wettach Court noted that the Bankruptcy Court had applied the Non-Necessities Approach, which we abandon today for certain situations in which an account is commingled. We explained that Mr. and Mrs. Wettach, who bore the burden of production,

produced no evidence to demonstrate how they spent the wages deposited into the entireties account. The bankruptcy court even offered them a "dollar-for- dollar reduction against any liability" for other deposits into the account

.... Having failed to carry their burden of production and absent clear error by the bankruptcy court, the Wettachs have no claim for relief on appeal.

Wettach , 811 F.3d at 111 (quoting Wettach , 489 B.R. at 507 ) (emphasis added). The "dollar-for-dollar reduction" for nonwage deposits refers to the formula dictated by the Non-Necessities Approach (Liability = Non-Necessity Spending – Nonwage Deposits).

For three reasons, however, this statement in Wettach does not mandate the Non-Necessities Approach for accounts that commingle wage and nonwage deposits.

First, the passage is not a ringing endorsement of the approach. We merely noted that the Bankruptcy Court "even offered" the Wettachs another potential offset. The statement is hardly a holding.

Second, even if the statement were taken as a holding, Wettach is distinguishable. It confronted a mixture of deposits much simpler than those facing us here: The Wettachs had produced "no evidence of any ‘other deposits.’ " See Titus III , 566 B.R. at 772 (discussing Wettach ). In other words, "the only deposits that proved to be at issue in Wettach were the wage deposits of the debtor." Id. As a result, the Wettach Court had no need to "directly address" the choice of method for measuring liability. Id. When the only source of funding into an account is wage deposits, there is no mystery about the source of a dollar spent on non-necessities, and thus no reason to consider a way of measuring liability like the pro rata approach. Hence Wettach does not bind us now.

Third, even the Wettach Bankruptcy Court expressed "some reservations" about the dollar-for-dollar offset dictated by the Non-Necessities Approach. Wettach , 489 B.R. at 507 (Agresti, J.). Bankruptcy Judge Agresti applied the approach only because a prior District Court decision had already approved it. See id. at 507–08 (citing Cohen , 487 B.R. 615 ). In yet another case arising out of the dissolution of the Titus firm, moreover, Judge Agresti had sounded the alarm about the dollar-for-dollar offset. See Oberdick , 490 B.R. at 710 n.15 ("The Court does have some concerns about the [Non-Necessities Approach] as to this point."). Were he "writing on a blank slate," he explained he would "give serious consideration" to employing "a presumption" in which "a pro rata share of the non-necessary expenditures could be deemed to have come from funds originating from the other deposits." Id. (emphasis added). Now faced with such a blank slate, we follow Judge Agresti’s prescient thinking.

* * *

In sum, the trustee missed his chance to challenge the use of the Non-Necessities Approach in the first appeal to the District Court. Hence his objection to the method for measuring liability has been waived. Going forward, however, courts faced with the situation here — in which wages and nonwages are commingled in a single account and are subsequently spent on both necessities and non-necessities — should apply a pro rata approach. They should presume, absent other evidence, that any spending out of the account was made up of a mixture of wage and nonwage dollars in proportion to the overall ratio of wage to nonwage deposits in the account.

C. Application of Non-Necessities Approach

Because the trustee waived his argument that another method should apply in calculating liability, we turn to the parties’ dispute over the application of the Non-Necessities Approach. To repeat, the approach proceeds from the assumption that all nonwage deposits into the account were spent on non-necessities before any wage deposits were impermissibly spent on non-necessities. This, in turn, informs its formula for fraudulent-transfer liability:

Liability = (Non-Necessity Spending) – (Nonwage Deposits) .

The final skirmish in the case centers on the last term in the formula: nonwage deposits. In the Bankruptcy Court, the parties stipulated that nonwage deposits could be divided into $634,998.83 of explained nonwage deposits and $268,167.09 of unexplained nonwage deposits. See Titus III , 566 B.R. at 798 ("The Parties agree that [the $268,167.09] were not wage deposits, but they also agree that other than being non-wage the source or sources of such deposits are unexplained."). In applying the Non-Necessities Approach, the Bankruptcy Court counted only explained nonwage deposits toward the "nonwage deposits" term in the formula. Had the Court also counted the $268,167.09 of stipulated unexplained nonwage deposits, the Tituses’ ultimate liability would have been reduced from $273,862.68 to $5,695.59. Thus the question presented in this section is whether the parties’ joint stipulation that the unexplained deposits were not wages was sufficient to meet the Tituses’ burden of production as to nonwage deposits.

To begin, we review the Bankruptcy Court’s decision on this point for clear error. See Wettach , 811 F.3d at 111. The Court did not commit clear error in the face of the "bright line rule" established by the District Court that "unexplained deposits may not be used to set off liability." Titus III , 566 B.R. at 768 ("[T]he District Court ... does not provide for any discretion in the matter — it provides there shall be no reduction for unexplained deposits."). In remanding the case for a second trial, the District Court made clear that the Tituses would need to "produce evidence about the source of the unknown funds" in order to offset their liability. Titus II , 498 B.R. at 521.

Aside from expecting the Tituses to follow this straightforward directive, there are at least three compelling reasons to apply a bright-line rule in situations like this. First, allowing an offset for unexplained deposits would "incentivize" debtors "not to come forward with any information that they had regarding the source of those funds," Cohen , 487 B.R. at 625, even though the debtor is "certainly in a better position than the [t]rustee to determine the source of the unexplained deposits," Titus IV , 2017 WL 5467712, at *6. Second, allowing an offset for unexplained deposits would allow debtors "to avoid judgment ... merely by having funds deposited into the account that could not be traced." Cohen , 487 B.R. at 625. Third, even a "nonwage" unexplained deposit could be a fraudulent transfer. "For example, if Paul Titus individually owned a rare painting, sold it for $268,167.09, and deposited the proceeds into the entireties checking account, those funds could not be used to offset objectionable expenses." Titus IV , 2017 WL 5467712, at *6 ; see also Titus III , 566 B.R. at 768 n.8.

In sum, we affirm the decisions of the Bankruptcy Court and District Court not to allow unexplained nonwage deposits to offset the Tituses’ liability.

IV. Conclusion

To recap, we reach three conclusions on the path to affirming the judgment of the District Court. First, fraudulent-transfer liability attaches to both Mr. and Mrs. Titus for the deposit of Mr. Titus’s wages from his law firm directly into the Tituses’ entireties bank account. The wage deposits into the account constituted a "transfer" under the PUFTA. Mrs. Titus is personally subject to fraudulent-transfer liability as a joint owner of the account. And Mr. Titus is subject to transferee liability even though he is the debtor-transferor as well. As a result, the wage deposits were a fraudulent transfer that the bankruptcy trustee could avoid.

Second, the trustee waived any objection to the Bankruptcy Court’s chosen method to calculate the Tituses’ liability. The Court followed the so-called Non-Necessities Approach, which holds that fraudulent-transfer liability is non-necessity spending less nonwage deposits, and the trustee did not challenge the approach in his first appeal to the District Court. Going forward for commingled accounts, however, the Non-Necessities Approach rests on an unreasonable expectation that a trustee can show by a preponderance of the evidence that a dollar of wages was impermissibly spent on a non-necessity. When deposits from different sources are commingled in an account, the Non-Necessities Approach almost always forces a trustee to explain the unexplainable. Absent other evidence, future courts instead should presume that any spending out of an entireties account is made up of a mixture of wage and nonwage dollars in proportion to the overall ratio of wage to nonwage deposits in the account. This pro rata approach accounts practically for the commingling of fungible funds and is not foreclosed by precedent in our Circuit.

Third, the Bankruptcy Court did not clearly err in its application of the Non-Necessities Approach. The District Court had set out a simple rule that the Tituses had to explain the source of their deposits into the account. Despite the parties’ stipulation that certain unexplained deposits were not wages, the Bankruptcy Court did not clearly err in refusing to offset the Tituses’ liability by the amount of those unknown deposits.

Thus we affirm.