At issue is the case of William Osborne, who was convicted in a brutal attack on a prostitute in Alaska 16 years ago. He won a federal appeals court ruling granting him access to a blue condom that was used during the attack. Testing its contents would firmly establish his innocence or guilt, says Osborne, who has admitted his guilt in a bid for parole.

But several justices said something more should be required, including a sworn declaration of innocence that would hold out the prospect of additional punishment for lying under oath.

One condition, Justice David Souter said, is that an "individual claiming the right to test claims that he is actually innocent."

People who waived DNA testing at the time of their trial also might not be able to test it later, some justices suggested.

The Obama administration, backing Alaska prosecutors, urged the court to reject the ruling of the federal appeals court in San Francisco in favor of Osborne.

Deputy Solicitor General Neal Katyal said the decision by the 9th U.S. Circuit Court of Appeals was too broad and would erase the requirement in the federal DNA testing law that a person must assert his innocence under penalty of perjury before getting access to the evidence.

Osborne has never made that claim and in fact admitted his guilt as part of his parole proceedings, Katyal said.

In an order Monday, the justices are ending Marcus Borden's fight against the East Brunswick, N.J., school district's policy that forbids him and other staff members from joining in student-led prayer. The federal appeals court in Philadelphia sided with the district.

The high court declined to weigh in on whether Borden's desire to bow his head silently and "take a knee" with his football players violates the Constitution's prohibition on government endorsement of religion. Borden says such gestures are secular.

The school district says Borden, the East Brunswick coach since 1983, had a long history of leading prayers before he was ordered to stop. The district says the issue is whether its policy is constitutional, not Borden's actions.

The 3rd U.S. Circuit Court of Appeals in Philadelphia agreed that the school district policy is constitutional, but the judges differed on what exactly the coach should do when his team prays.

The case is Borden v. School District of the Township of East Brunswick, 08-482.

U.S. District Judge Susan Illston ordered last week that the answers provided on the forms, which are intended to root out bias in selecting a jury, should be off limits to the public. There are more than 60 questions on the forms including potential jurors' opinion of Bonds and whether they've followed the issue of steroid use in professional sports.

The forms also include a potential juror's name, age, gender, level of education, job, criminal record and any ethical, religious or political views that would influence the juror's decision making, as well as other personal information.

The Associated Press, ESPN, Hearst Corp., The New York Times Co., ABC-subsidiary KGO, KNTV Television Inc., NBC subsidiary KNBC-TV, The Los Angeles Times, the Medianews Group and Sports Illustrated publisher Time Inc. filed court papers seeking public access to the forms.

Media company lawyers argued that the questionnaires should be considered part of the jury-selection process, which is required to be done in open court. The lawyers noted that neither Bonds' lawyers nor federal prosecutors have asked the judge to seal the documents.

"Here, there is no valid basis for keeping the public in the dark about the answers provided by prospective and trial jurors," the papers stated.

The home run king's trial begins Monday, when potential jurors throughout the Bay Area are summoned to the federal courthouse in San Francisco to fill out the forms. The slugger's lawyers, prosecutors and the judge will question them in person about their answers beginning on Tuesday.

In a ruling announced Wednesday, a New York judge says trustees managing Helmsley's estate can distribute her funds to a broad range of charities.

Helmsley died in August 2007. She left instructions in one of the documents relating to her charitable trust that money be donated to help care for dogs, as well as other charities.

Manhattan Surrogate Court Judge Troy Webber ruled that trustees of the Leona M. and Harry B. Helmsley Charitable Trust have sole discretion for which charities should get the Helmsley fortune.

Trust spokesman Howard Rubenstein says the trustees will announce the first grants from the foundation next month.

In a 7-2 vote, the court ruled that a federal appeals court in Richmond, Va., wrongly threw out the conviction of Randy Edward Hayes. Justice Ruth Bader Ginsburg wrote the majority opinion. Chief Justice John Roberts and Justice Antonin Scalia dissented.

The federal government, gun control groups and women's rights advocates worried that a ruling for Hayes would have weakened the federal law enacted in 1996 that applied the 40-year-old ban on gun possession by a felon to people convicted of domestic violence misdemeanors.

The 4th U.S. Circuit Court of Appeals ruled in Hayes' favor because the West Virginia state law on battery under which he was convicted did not contain specific wording about a domestic relationship between the offender and the victim.

Nine other appeals courts rejected that interpretation.

The justices, in an order Monday, are refusing to hear FTC's plea to reinstate the commission's ruling that Rambus, based in Los Altos, Calif., violated antitrust law.

A federal appeals court in Washington overturned the FTC ruling last year.

The Bush administration had declined to back the FTC in its appeal to the high court.

Supporters of both Democrat Al Franken and Republican Norm Coleman see a winner influencing the balance of power in the Senate, even as the Democrats already firmly hold the chamber.

"The 59th vote in the Senate is very valuable, and that's obvious now," said Kathryn Pearson, an assistant professor of political science at the University of Minnesota. "It's valuable for Democrats to add a vote, and it would be very valuable to Republicans to deny that vote."

For Democrats, the absence of Franken's vote has already made passing legislation more of a challenge. The $787 billion stimulus bill squeezed through the Senate late Friday night on the vote of Sen. Sherrod Brown, D-Ohio, who was flown back to Washington on a government plane from his home state, where he was mourning the death of his mother. Democratic Sen. Edward M. Kennedy of Massachusetts, who is suffering from a brain tumor, could not attend the vote.