The city owns some of the narrowest, most unusual lots in New York.

Some of the land has been vacant for decades, even as affordable housing options have dwindled and luxury apartments have risen nearby, for at least one good reason: Nobody has wanted to build there.

Whether it is the result of development leftovers or zoning quirks, building code challenges have often made these lots undesirable to private investors.

Now the city is turning to architects, not developers, for help: On Monday, the Department of Housing Preservation and Development will announce a design competition for ideas on how to create affordable housing on 23 of these small, irregular lots.

The department hopes the winning entries will help solve design problems at other lots where site challenges have curtailed building. But the question of just how affordable these homes will be when they are finished has some residents wary.