CHICAGO — Perhaps it’s not fair, given all the temptation on the beat from deep-dish pizza and Chicago-style hot dogs (that’s with pickles and tomatoes) and with vast parts of the city smelling of chocolate thanks to a downtown candy factory.

But the skinny on the officers of the Police Department here, at least according to the new police superintendent, is that some have, let’s say, fitness issues.

The superintendent, Jody P. Weis, a former F.B.I. agent, came in last month as a reformer vowing to clean up the nation’s second-largest police force, and has already diversified the ranks and bolstered community relations. Now Mr. Weis, an exercise enthusiast, has shocked more than a few people with talk of mandatory fitness tests and maximum body-fat allowances (only after a year’s physical education and with exceptions, of course).

Mr. Weis has said he wants only to promote healthful physical standards. But some officers think he hasn’t been around long enough to judge their true condition.

“I hope it’s not his opinion that this force is in bad shape as compared to others,” said Mark P. Donahue, president of the Chicago local of the Fraternal Order of Police. (Police departments across the country have long struggled with the problem of overweight officers; a chief in Florida lost his job in 2006 after sending a memo to his officers titled “Are You a Jelly Belly?”)

Mr. Donahue would not comment further, as negotiations on Mr. Weis’s proposal continue.

The officers’ union has taken a stab at why some officers may be overweight, pointing to emotional eating, a result, it says, of job-related stress. And some officers want Mr. Weis to cut one hour off every workday to devote to exercise.

They also like the idea of putting kitchens in the station houses. That way, officers could cook their own food and be less reliant on things like pizza and hot dogs, whatever the style.