The Supreme Court is considering a case concerning legislation that says victims of pornography deserve restitution. (MICHAEL REYNOLDS/EPA)

A woman with the pseudonym Amy Unknown was at the Supreme Court on Wednesday as justices discussed the horrible events that changed her life: Her uncle raped her when she was a young girl, recorded that assault and other sex acts and put the images on the Internet, where they have been viewed tens of thousands of times.

All the justices seemed to think that those who downloaded the images of Amy should pay to help her put her life back together. But they struggled to decide what any one person should pay.

Congress made it clear in 1994 that victims such as Amy deserved restitution from those who have viewed the pornographic images that feature them. The cost of Amy’s abuse, according to a psychological report that described her trauma and ongoing counseling and medical treatment, is $3.4 million.

The immediate question before the justices was how much of that should be paid by a Texas man named Doyle Randall Paroline.

Paroline pleaded guilty in 2009 to possessing 300 images of child pornography, including two of Amy. He was sentenced to prison. And on the matter of how much money he owes Amy, the U.S. Court of Appeals for the 5th Circuit said all $3.4 million.

The court based its decision on a section of the law that said courts are directed to make the defendant pay “the full amount of the victim’s losses.” The court’s reading of the law conflicts with those of other courts, but Amy’s attorney Paul G. Cassell said it was proper.

“Congress wanted to take these vulnerable victims — child pornography crimes, federal sex offense crimes and domestic violence — and get them full restitution as quickly and effectively as possible,” said Cassell, a law professor at the University of Utah and a former federal judge.

Some justices said Congress surely meant that courts should consider how much a defendant had contributed to the victim’s suffering.

“He’s guilty, he’s guilty of the crime,” Justin Antonin Scalia said of Paroline. “But to sock him for all of her psychiatric costs and everything else because he had two pictures of her? Congress couldn’t have intended that.”

But Cassell said Congress could not have intended to send Amy on the hunt for defendants to sue. Alerted by the government when an image of her is discovered, it has taken Amy 41 / 2 years to collect $1.75 million, from 182 defendants ($1.2 million came from one man). Cassell said it is estimated that more than 70,000 people have seen Amy’s image.

If each defendant was tagged with the total cost, Cassell said, Amy might receive the restitution quickly from one or more wealthy individuals. The hunt would then be over, and she would receive no more than the $3.4 million the court approved.

Paroline’s attorney, Stanley G. Schneider, on the other hand, said his client should not have to pay anything, which is what a district judge decided.

Schneider, who was appointed by the court to represent Paroline, said so many people have seen Amy’s image that the government could not prove it was Paroline who has caused her suffering.

Justice Elena Kagan said that could not be right.

“If only one person viewed the pornography, that person would be responsible for the entire damages, but if 1,000 people viewed the pornography and the harm was that much greater, nobody would be on the hook for restitution?” she said. “How could that possibly make sense?”

But if the obvious compromise was somewhere between zero and everything, the court had trouble deciding precisely where.

Such a middle ground is what the federal government urged. But Deputy Solicitor General Michael R. Dreeben acknowledged that there was no easy formula. One possibility would be to divide the victim’s restitution by the number of defendants convicted.

But Justice Ruth Bader Ginsburg pointed out that would not include future defendants.

And Chief Justice John G. Roberts Jr. noted another problem, asking, “How does that work for the first person” convicted?

“It doesn’t work very well for the first person, Mr. Chief Justice,” Dreeben replied.

Dreeben said judges could look at what their colleagues had done in similar situations, just as they sometimes do in imposing prison sentences. But Kagan wondered whether those were simply numbers “plucked from the air.”

Ginsburg pointed out that Amy’s uncle, the perpetrator of the crime, served prison time but paid only about $6,000 toward counseling. Justices Stephen G. Breyer and Samuel A. Alito Jr. voiced similar concerns about how to divide restitution.

Cassell said those were not Congress’s concerns.

“If there was a wealthy defendant who was unhappy with the share he’d been ordered to pay, he could simply try to find other wealthy defendants out there and interplead them in some kind of a case,” Cassell said. “We admit that’s going to lead to litigation burdens, [but] Congress wanted those burdens on guilty criminals rather than innocent victims.”

The case is Paroline v. United States.