“What this school official did,” Mr. Wolf said, referring to the male assistant principal who ordered the search, “was act on nothing more than a hunch — if that — that Savana was currently concealing ibuprofen pills underneath her underpants for others’ oral consumption.”

“I mean, there’s a certain ick factor to this,” Mr. Wolf said.

Without intimating a view on the ickiness of what Mr. Wolf had described, Chief Justice John G. Roberts Jr. suggested that the law might treat different undergarments differently. “The issue here covers the brassiere as well,” he said, “which doesn’t seem as outlandish as the underpants.”

Justice Breyer elaborated on what children put in their underwear. “In my experience when I was 8 or 10 or 12 years old, you know, we did take our clothes off once a day,” he said. “We changed for gym, O.K.? And in my experience, too, people did sometimes stick things in my underwear.”

The courtroom rocked with laughter, and the justice grew a little flustered at having apparently misspoken.

While Supreme Court arguments can often be bone-dry exercises in statutory exegesis and doctrinal refinement, Tuesday’s session was grounded in vivid facts: school snitches, drugs, underwear and body cavities.

None of the lawyers had a particularly easy time of it. Matthew W. Wright, representing the school district, said that intimate searches should be allowed even for the most common over-the-counter drugs.

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“At some point it gets silly,” Justice David H. Souter said. “Having an aspirin tablet does not present a health and safety risk.”

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Mr. Wright did draw the line at searches of students’ body cavities, but only on the practical ground that school officials are not trained to conduct such searches. Mr. Wright said there was no legal obstacle to such a search.

David O’Neil, an assistant to the solicitor general representing the federal government, tried to steer a middle course.

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The Fourth Amendment had been violated, he said, because school officials did not have a reasonable suspicion that Ms. Redding had secreted drugs in her undergarments. But Mr. O’Neil added that Ms. Redding should not be allowed to sue the assistant principal who ordered the search, because the law was unclear at the time.

Justice Antonin Scalia challenged him on the first point.

“You search in the student’s pack, you search the student’s outer garments, and you have a reasonable suspicion that the student has drugs,” he said. “Don’t you have, after conducting all these other searches, a reasonable suspicion that she has drugs in her underpants?”

“You’ve searched everywhere else,” Justice Scalia said. “By God, the drugs must be in her underpants.”

Mr. O’Neil said a more focused suspicion was required. “Certainly there is no practice anywhere, that I’m aware of, of hiding ibuprofen in underwear,” he said.

On the other hand, if there is good reason to think a student is keeping contraband in her underwear, Mr. O’Neil said, “you could go directly to that location.”

That surprised the chief justice. “Oh, surely not,” he said. “You are saying if you have reasonable suspicion that it’s in the underwear, you shouldn’t even bother searching the pack or the pockets? You should go straight to the underwear? That can’t be right.”

Mr. Wolf, Ms. Redding’s lawyer, injected another new term into the court’s lexicon. He said a search may be appropriate if the school has evidence that a student makes a habit of “crotching” drugs.

Justice Souter may have summarized the mood of the court near the end of the argument in the case, Safford Unified School District v. Redding, No. 08-479. Several justices appeared troubled by the search, but also seemed loath to second-guess school officials confronted with a variety of dangerous substances.

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“My thought process,” Justice Souter said, “is I would rather have the kid embarrassed by a strip search, if we can’t find anything short of that, than to have some other kids dead because the stuff is distributed at lunchtime and things go awry.”