As Mayor Bloomberg approaches the final year of his first term, labor leaders say he is proving a more formidable negotiator than his famously tough-talking predecessor.

Mr. Bloomberg struck a deal with the largest city union, District Council 37, but he’s been unable to strike accords with the politically potent police, fire, and teachers unions. Earlier this year, the teachers held a big rally to try to put pressure on the mayor, and some members of the police and fire unions took to following him around and heckling him. None of that worked.

“He’s tough, and there’s lots of things I haven’t liked about what he has done, but he’s more formidable,” the president of the United Federation of Teachers, Randi Weingarten, said of the current mayor.

After Mr. Bloomberg was elected, labor leaders were anxious to see if the billionaire businessman’s entrepreneurial experience would improve the historically strained relationship between City Hall and the unions. That has not happened.

“Bloomberg is Giuliani with a smile,” the president of the Patrolmen’s Benevolent Association, Pat Lynch, said through a spokesman.

Exercising their special rights under state law, the police and firefighters recently asked that their raises be determined through binding arbitration. The teachers, though, have to deal with the mayor.

While city officials have refused to comment publicly on the negotiations, it’s clear the city has been trying to scale back the teachers’ restrictive, 200-plus-page contract, which governs everything from pay to seniority rights to preparation time. For example, while the contract does not provide for merit pay, the schools chancellor, Joel Klein, has talked frequently of late about his desire to pay good teachers extra.

A teachers deal could be close, according to recent reports. Ms. Weingarten said in an interview late last week, however, that after 17 months without a contract, the negotiations were “very, very tough going.”

The last contract the teachers negotiated with Mr. Giuliani was in the mid-1990s, and it left the union resentful. In the fall of 1995, the mayor convinced union leaders that the city was short on funds and couldn’t grant teachers raises for two years. But in December, just as the union was about to approve the contract, Mr. Giuliani announced he was granting large raises to managers, and the talks dissolved. In May, the union ended up ratifying a five-year contract that looked much like the one they almost voted on in December.

“There was never any trust between the UFT and the mayor after that, certainly on the UFT’s side,” Ms. Weingarten said.

The next contract the union agreed to came in June 2002, once Mr. Bloomberg was in office. It gave the teachers raises retroactive to 2000, when the last contract had expired, and raised the annual starting salary for certified teachers by 22%.

In contrasting the negotiating styles of the two Republicans who have been the city’s mayor for the past 11 years, Ms. Weingarten said that while Mr. Giuliani reacted at the bargaining table to public feuds, Mr. Bloomberg is less swayed by the public histrionics that often accompany New York City labor negotiations.

“You really have to spend a lot of time, energy, and effort, very privately, trying to think through issues,” she said. “You know that when you do the arguments publicly, that you’re not making any private progress. It’s just a very different kind of style.”

After the teachers’ last contract expired in May 2003, Ms. Weingarten held press conferences to discuss her demands. That, she quickly learned, was not an effective tactic with this mayor.

“You have not heard me talk very publicly about anything of late, when we’re in negotiations,” she said.

Other union leaders have had the same experience.

“You’re better off not negotiating in the press,” the executive director of DC 37, Lillian Roberts, said.

Ms. Roberts and Ms. Weingarten both said the only way to persuade Mr. Bloomberg is by presenting compelling facts, not by issuing threats or orchestrating protests.

“We haven’t been able to convince him about micromanagement in the schools and some other things, but when we were able to convince him, for example, about security, look what happened, things have gotten better,” Ms. Weingarten said. “He has an engineering mind, and it takes a lot of facts to convince him. But I also find him to be honest and forthright.”

Ms. Weingarten said much of the difference between Messrs. Bloomberg and Giuliani in styles of negotiation could boil down to politics.

Mr. Giuliani never had control of the schools, which were run by a Board of Education dominated by appointees of the borough presidents.

But Mr. Bloomberg’s top priority when he took office in 2002 was convincing the state Legislature to give him control of the schools, and Mr. Bloomberg has said very directly that voters should decide whether to re-elect him based on his record on education.

“Certainly the rhetoric has toned down in the last month or so – the teachers want a deal and the mayor wants to make a deal,” a political consultant, Hank Sheinkopf, said. “Politically, he needs to get it done long before the election.”

The next bargaining session is scheduled for next week, precisely one year before the election that will determine if Mr. Bloomberg gets four more years in City Hall.