NEW YORK -- Just four days before baseball players were scheduled to strike, the sides stopped their public posturing and instead devoted Monday to a series of meetings that went on into the night.

Owners made small steps to the union in their latest offer Sunday, and it appeared the next move was up to the Players' Association, which didn't immediately respond to the new proposal.

The sides met Monday afternoon, again in the evening and briefly again Tuesday morning. Negotiators, who took pointed jabs at each other in public comments after exchanging proposals last weekend, were suddenly silent.

"We had some informal conversations, that's it," Gene Orza, the union's No. 2 official, said without disclosing any details.

Some players thought a faction of hardline owners still doubted players would go through with their strike, scheduled to start with Friday's games.

"I don't know if they think we're bluffing," Los Angeles Dodgers player representative Paul Lo Duca said. "We never have before."

Time was running short for a settlement that would prevent baseball's ninth work stoppage since 1972. During the weekend, the sides reacted angrily to each other's proposals.

"It was a tough night for us a couple nights ago,'' Boston's Johnny Damon said. "We are definitely bridging the gap and, hopefully, we can continue to play baseball.''

From a logistical standpoint, Players' Association officials have suggested to ESPN that a deal virtually has to be in place by sometime Wednesday in order to avoid a strike at week's end.

"My sentiment hasn't changed -- I'm an optimist by nature," New York Yankees player representative Mike Stanton said. "There are proposals from both sides and concessions from both sides. Albeit small, a concession is a concession."

In 1994, the sides didn't start bargaining until three months after the start of strike, which dragged on for 232 days and led to the first cancellation of the World Series in 90 years.

"There's been a good dialogue," Boston's Tony Clark, the AL player representative, said Monday night.

Negotiators spent the day discussing the key economic issues, one management official said, speaking on the condition he not be identified.

"I think we're a lot closer than what we hear in the media," said Brandon Inge, Detroit's assistant player representative. "I honestly don't think we will go out. I hope not. I think we are fairly close and have made a lot of progress from where we started. Even if it goes down to the last day, as long as we get together, it will be a good thing."

Owners want vastly increased revenue sharing and a luxury tax to slow the spending of high-payroll teams. Players have agreed to revenue sharing increases, but proposed a lower level than management and asked to phase in the changes, which management opposes.

On the luxury tax, owners want higher tax rates and lower thresholds than players. Owners regard the union's proposal as ineffective and players think management's plan would act like a salary cap.

Owners increased the tax threshold Sunday from $102 million to $107 million in the first three years of the new contract and to $111 million in 2006. The portions of payrolls above that figure would be taxed, using the average annual value of 40-man rosters plus about $7.7 million per team in benefits.

Players have proposed thresholds of $125 million next year, $135 million in 2004, $145 million in 2005 and no tax in the final season of the deal -- another big point of contention.

Owners gave proposed tax rates of 35-50 percent, depending on the number of times a team exceed the threshold, while players have proposed rates of 15-40 percent.

As for revenue sharing, owners proposed that teams share 36 percent of their locally generated revenue, up from 20 percent this year. The teams' previous plan was 37 percent, and the union moved up to 33.3 percent in its Saturday proposal.

The owners' plan would transfer $263 million annually from baseball's richest teams to its poorest, using 2001 revenue figures for analysis. Because the union's proposal phases in changes, the players' proposal would transfer $172.3 million in 2003, $195.6 million in 2004, $219 million in 2005 and $242.3 million in 2006.

The Associated Press contributed to this report.