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NEW YORK – With a week to go, negotiators for players and owners expressed optimism that they have enough time to reach a deal and avoid another baseball strike. 

The sides had three bargaining sessions Thursday, completing an agreement on debt regulation that eased the union’s concerns the rules would restrict spending on players. The union didn’t respond to the owners’ latest revenue-sharing proposal but said it will soon. The players’ executive board was to discuss the talks during a telephone conference call Friday. 

“The issues have been narrowed sufficiently that it would not take very much time to conclude an agreement,” said union lawyer Steve Fehr, the brother of union head Donald Fehr. 

While the sides are still apart on their revenue-sharing proposals and disagree on the levels of a proposed luxury tax on the payrolls of baseball’s biggest spenders, they agree on much of the framework. 

Sometime next week, the sides must decide whether they want to compromise on their numbers or try to outlast each other during a strike. If players walk out on the Aug. 30 strike date, it would be baseball’s ninth work stoppage since 1972. 

“We have plenty of time to resolve all of the issues that are outstanding between the parties,” said Rob Manfred, the owners’ top labor lawyer. “It’s just a difference of numbers. ... Seven days is plenty of time to resolve those numerical differences.” 

Much of Thursday, according to Manfred, was devoted to scheduling, interleague play and the assignment of player contracts. 

The debt regulation agreement resolved a potential problem with the owners’ 60-40 rule, according to a management official who spoke on the condition of anonymity. 

The 60-40 rule, established in the mid-1970s but enforced only periodically, requires each team to have at least 60 percent of its value in assets and no more than 40 percent in debt.