Pink slips will soon be on their way to Los Angeles city workers now that Mayor Antonio Villaraigosa and his general managers have finalized the first list of 542 positions slated for elimination.

In a memo to 13 general managers Wednesday, Villaraigosa's chief of staff, Jeff Carr, ordered each agency head to immediately sign off on the proposed layoff list for his or her department, and said he expected "full cooperation" with the directive. The move is intended to help close the city's $212-million budget shortfall this fiscal year and help shrink next year's $485-million gap.

"If there was any doubt that that city is moving forward on the original 1,000 position eliminations, this confirms that we are moving forward on that," said City Administrative Officer Miguel Santana. He added that department heads must now determine whether workers in those positions have already been transferred to other positions.

The initial list includes the elimination of 89 child-care workers in the parks department, more than 100 messengers, clerks and librarians in the library department, and about 50 tree surgeons in the bureau of street services (some of whom may move to the Department of Water and Power).

Many of those job eliminations won't happen until July 1, however, because the workers are protected by an agreement struck last year between city leaders and the Coalition of L.A. City Unions. In the next few months, the most vulnerable workers are those who are not represented by any union or employees who are part of the Engineer and Architects Assn.

Though the City Council approved the elimination of 4,000 positions last month, the list initiating the process seemed to catch some members off guard. Flipping through the thick document on the council floor, Councilman Bill Rosendahl questioned the logic of the list drawn up by general managers and the mayor's staff.

"Are these the right jobs to eliminate especially if we want our trees trimmed, our parks open, our libraries going, or is there is another strategy within the department that can be used?" Rosendahl said. "It definitely means a cutback in services."

Officials said they expect to finalize the remaining positions on the 1,000 job cut list within the next few days. The mayor plans to outline the 3,000 additional job cuts when he presents next year's budget, which is due next month.