Mr. Lynch's goal is to pressure the mayor into giving raises considerably larger than those received by the other uniformed unions.
In July 2001, leaders of the firefighters' union had agreed to a tentative settlement along the lines of those accepted by most uniformed unions.
But the heads of the major uniformed unions quickly denounced the idea of a wage freeze.
The uniformed unions usually held out for a bit more.
Only contracts with the uniformed unions and a variety of smaller unions remain to be negotiated in the months ahead.
Indeed, he has yet to negotiate contracts with the uniformed unions, including police and fire.
But in Albany, where the uniformed unions hold great sway over legislators, every reform effort has failed.
The uniformed unions have been without contracts since November 1991.
Mr. Giuliani has a fresh chance to reach labor peace with the uniformed unions.
In December, the city was involved in intense negotiations with a coalition of uniformed unions that was asking for far less than the police.