The 1994 law allows victims of child pornography to seek the “full amount” of their losses from people convicted of producing, distributing or possessing it, and Amy asked the United States District Court in Tyler, Tex., to order Mr. Paroline to pay her the full $3.4 million.

Mr. Paroline said he owed Amy nothing, arguing that her problems did not stem from learning that he had looked at images of her. Amy’s uncle, who was sentenced to 12 years in prison for his crimes, bore the brunt of the blame, Mr. Paroline said, but was ordered to pay Amy just $6,325.

He added that Amy’s “problematic behavior,” including drinking and troubles at work and school, could have sources other than her “sexual abuse history.”

Mr. Paroline was sentenced to two years in prison, but the trial judge, Leonard Davis, did not order him to give Amy anything. The link between Amy’s losses and what Mr. Paroline did, Judge Davis said, was too remote.

The United States Court of Appeals for the Fifth Circuit, in New Orleans, disagreed and awarded Amy the $3.4 million she sought. Mr. Paroline should pay what he could and seek contributions from his fellow wrongdoers if he thought it too much, the court said, relying on the legal doctrine of “joint and several” liability.

“Among its virtues,” the appeals court said, “joint and several liability shifts the chore of seeking contribution to the person who perpetrated the harm rather than its innocent recipient.” In the long run, Amy would not receive more than she deserved. But nor would she have to chase hundreds of men, many of them penniless, for the fractional shares of her misery that they caused.

Mr. Paroline said the ruling was deeply unfair. “An award of $3.4 million against an individual for possessing two images of child pornography is punitive and grossly disproportionate to the offense conduct,” he told the Supreme Court. Requiring him to seek payment from his fellow sex offenders, he added, “would create a procedural nightmare.”