New Yorkers routinely grouse about living in apartments roughly the size of a closet. Under a city contest announced Monday, that complaint might not be such an exaggeration.

A new competition launched by Mayor Michael Bloomberg calls for plans to develop dozens of so-called micro-units, studio apartments that go beyond cozy to downright compact: 275 to 300 square feet.

Or, to put it in perspective, about 41 times smaller than the mayor's Upper East Side town house.

Such Lilliputian living quarters aren't currently allowed under city zoning laws. But under the pilot program proposed by the mayor, officials will waive regulations at a city-owned site in Manhattan's Kips Bay neighborhood to test the market. The Department of Housing Preservation and Development is seeking proposals to design, construct and operate the micro-unit rental building at 335 E. 27th St.

Mr. Bloomberg said there is significant demand for smaller homes. New York City has 1.8 million one- and two-person households, but only one million studio and one-bedroom apartments, officials said. The crunch has led to a spate of illegally subdivided apartments.