In New York, one of the most expensive cities for new development, there are acres of vacant land on irregular lots considered too narrow, too shallow or too onerous to build on. Like the offal left after the prime cuts of meat, they are the odds and ends that take the most skill to manipulate.

But with land prices near all-time highs, developers and nonprofit housing groups are giving the leftovers another look. In some cases, building on odd lots can mean a rare chance to get into high-demand neighborhoods. In others, the lots can represent a relatively inexpensive way to build below-market-rate housing. The city has long grappled with how to deal with vacant public land that comes into its possession — often through unpaid taxes — even as the need for affordable housing has grown.

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The city, too, is contending with vacant land use issues, and not always on the scale of large developments. In early 2018, the City Council passed Local Law 29, which will require a citywide survey of vacant residential buildings and lots, not including flood zones, to be released sometime in 2021.

And this month, the Department of Housing Preservation and Development announced a design competition for ideas on how to create affordable housing on 23 small, publicly owned lots in the five boroughs, many in quickly gentrifying neighborhoods. One of the goals is to learn how to build housing on other difficult lots in the city, public and private.