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Note that the disgorgement provision of the Lanham Act expressly addresses burden shifting (unlike the Copyright Act and § 289 of the Patent Act): "In assessing profits the plaintiff shall be required to prove defendant’s sales only; defendant must prove all elements of cost or deduction claimed."

law.cornell.edu/uscode/text/15

So this provision provides the best support for the "we can't prove their profits so give us the whole account" argument.

LII / Legal Information Institute15 U.S. Code § 1117 - Recovery for violation of rights

I'm not saying that's a good argument. Only that it's strongest in Lanham Act cases.

Sarah Fackrell

And the underlying decision (by Judge Seeger): storage.courtlistener.com/reca

"The Court declines the request to award profits because Plaintiff offered evidence of revenue, not profits. Revenue and profits are not the same thing. The Court declines the invitation to assume that all of the revenue equals profits."