When Mayor Bill de Blasio announced his first labor agreements with New York City unions this spring, he was sharply criticized for granting long-awaited wage increases in exchange for promises of unspecified though sizable savings on health care expenses.

Now, some of the specifics are coming into focus: City officials and union leaders say they hope to push municipal workers to use walk-in clinics more and emergency rooms less, order generic drugs more often than brand-name ones, and buy them through the mail rather than at retail pharmacies to achieve bulk discounts.

The city hopes the unions will agree to steer workers to use centralized, cheaper centers for blood tests, X-rays or M.R.I.s, rather than having those tests performed in doctors’ offices or at costly physician-owned facilities. Patients who resist could face higher copayments, while savings would be passed on to the city in lower premiums.

The cost-cutting comes with high stakes: If the city and unions are unable to save a total of $3.4 billion on health care by 2018, a mediator will be empowered to order increases in workers’ premiums to cover the shortfall, officials said.

As an added inducement, if the unions help the city exceed that goal, the first $365 million in additional savings would be distributed as lump-sum bonuses to workers, officials said. Any savings beyond that would be split evenly between the city and its employees.

In interviews, Harry Nespoli, chairman of the Municipal Labor Committee, the umbrella group of city unions, and Robert W. Linn, the city’s labor relations commissioner, disclosed several of the cost-saving measures being discussed as the two sides draw closer to a deal.

For example, union officials are meeting with EmblemHealth, an insurer that covers many municipal union members, to negotiate increased access for employees to EmblemHealth’s more than 40 walk-in clinics across the city.

Arrangements like that could reduce costly emergency-room visits not only for the city’s 350,000 workers but also for their dependents — a total of about one million people, the officials said.

Missing from the labor contracts with teachers and other city workers that were announced beginning in May was any requirement for union members to begin contributing toward their health insurance premiums. That prompted some critics to say Mr. de Blasio was not being tough enough at the bargaining table.

Earlier this month, the Metropolitan Transportation Authority and the unions representing 5,400 Long Island Rail Road employees agreed that those workers would begin paying 2 percent of their wages toward their health coverage.

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Jeffrey R. Ungvary President