NEW YORK -- Negotiators for baseball players and owners are making slow progress to narrow their differences, and the union keeps holding off on setting a strike date.

Starting what could be a pivotal week in talks to avoid a strike later this month or in September, the sides devoted two of Monday's three bargaining sessions to revenue sharing, one of the key issues dividing them.

"I would expect the pace of the activity to be heightened this week," said Rob Manfred, the owners' top labor lawyer.

The second of the three sessions produced agreements on some minor issues, such as waiver periods and second medical opinions.

"We're still looking for the right way to bridge the gaps," union lawyer Michael Weiner said. "We haven't found it yet."

Later this week, according to Weiner, players will respond to management's proposal for mandatory random testing for steroids and other performance-enhancing substances.

The union's executive board scheduled a conference call for Tuesday but was unlikely to set a strike date, according to people familiar with the union's deliberations.

However, if there is not much progress this week, the executive board could meet Aug. 12 in Chicago -- the eighth anniversary of the start of the 1994-'95 strike -- and it's possible a strike date could be set then.

Players fear that without an agreement to replace the one that expired Nov. 7, owners would change work rules or lock them out after the World Series. The union wants to control the timing of a stoppage, preferring late in the season, when more revenue would be threatened.

Owners want to increase the percentage of shared locally generated revenue from 20 to 50 percent. The sides differ on both dollars and structure.

"We have gone days where we have not moved in the wrong direction in this topic. I really do believe this topic is resolvable," Manfred said, adding that there was plenty of "middle ground."

Owners also want a 50 percent luxury tax on the portions of payrolls above $98 million, which figures to be the most divisive issue. The union thinks a luxury tax, especially when combined with increased revenue sharing, would drain money from the high-revenue teams, who otherwise would spend it on players.

The sides agreed that players with less than five years of major league service can be directed for no more than 20 days to undergo baseball-related rehabilitation at a team's spring training facility.

However, starting with the 11th day, each day at the spring training site would be deducted from the limit on a rehabilitation assignment to the minor leagues for the player, currently a maximum of 30 days for pitchers and 20 for others.

That subject became a dispute two years ago when Kansas City's Carlos Beltran refused to go to the Royals' spring training site, and the team attempted to suspend him.

Players and owners also agreed to eliminate a restriction on players' ability to get second medical opinions at the expense of his team. A rule that divided the United States into three regions, and required a player to pay for his transportation if he went out of his region, will be eliminated.

The sides also agreed to divide the year into four waiver periods instead of three. The current periods are Nov. 11 to day 30 of the season, day 31 to July 31, and Aug. 1 to Nov. 10. The first period will be divided into Nov. 11 to Feb. 15, and Feb. 16 to day 30.

In addition, the sides agreed to allow the commissioner's office to mail contracts to all players on behalf of clubs on Dec. 20 instead of having the teams mail the contracts individually.

The sides moved close to an agreement on deferred compensation. Currently, teams must fund deferred payments by the fourth year after the season in which they are earned.

Owners have proposed that it be funded by the start of the second year after the money is earned, while players have countered with Nov. 1 in the second year after it is earned.

The sides are close to an agreement on the benefits plan and the minimum salary, which will rise from $200,000 to between $285,000 and $300,000.

"We are closing in," Manfred said. "It's just a matter of time until we finish those off."