The NFL and its locked-out players wrapped up another round of court-ordered mediation Tuesday without any signs of a new agreement and the clock ticking on the 2011 season.

Officials and attorneys for both sides said they will return for more closed-door talks with U.S. Magistrate Judge Arthur Boylan on June 7, four days after a key appeals court hearing in St. Louis on the legality of the lockout.

NFL lead negotiator Jeff Pash and Hall of Famer Carl Eller both said the talks went well, but there was no indication of any significant progress toward a new collective bargaining agreement. Pash said he thought Boylan had done a good job of "pushing the parties," but he said he doesn't believe the dispute over the future of the $9 billion business will be settled in court.

"The only way we're going to solve this is by sitting down together," Pash said, echoing the NFL's preference for traditional negotiations in a collective bargaining setting and adding: "We owe it to our game. We owe it to our fans. We owe it to each other, to the players and to the clubs, to sit down and negotiate."

A San Diego-based defense contractor pleaded guilty Monday to offering bribes to a Navy official who, in return, placed $300,000 worth of orders from the company for military aircraft.

Jesse Denome, owner of JD Machine Tech, Inc., admitted that from June 2004 to September 2005 he gave a Navy official a bicycle worth nearly $2,500, a model airplane engine worth $449 and made $18,000 in payments on the official's personal credit card.

In exchange, prosecutors say the official placed over 100 orders from the company for a Navy's aircraft program.

The Navy is still investigating the official, identified only as D.V.

Prosecutors say Denome was trying to illegally win valuable Navy contracts over the competition.

According to court documents, Denome also filed false tax returns in 2005, 2006 and 2008, claiming $300,000 less than his income and passing off vacations and hobbies as business deductions. Prosecutors say as a result, he owes the government more than $80,000.

Denome, 47, faces up to eight years in prison and more than $500,000 in fines. He is scheduled to be back in court for sentencing in August.

The Supreme Court has declined to hear a dispute over whether students challenging a private Hawaiian school system's admissions policy must be identified.

The court on Monday left in place lower court rulings against four non-Hawaiian students who object to the Kamehameha Schools' policy that gives admissions preference to those of Hawaiian ancestry. Only a few non-Hawaiians have ever been admitted.

The challengers wanted to file their suit anonymously because of concerns about public humiliation and retaliation if they are identified.