The design for the cluster of small houses, with their pitched roofs and clapboard siding, looks like something from another era of New Orleans architecture, but the plan for these “Carpet Cottages” is brand new. It’s a plan that fits 14 single-story homes, plus parking spaces, onto less than half an acre.

The Carpet Cottages are just the latest twist on densely developed attached housing with four or fewer stories. The growing shortage of land in many markets and the spreading prevalence of infill housing is squeezing low-rise buildings into surprisingly old-fashioned shapes as conventional breezeway garden apartments lose their usual setbacks from the street, their diagonal orientation, and their chunky facades—and begin to look very much like traditional townhouses.

Developers have quickly picked up on the townhouse revival as sites suitable for garden apartments become increasingly difficult to find in many markets. “‘Garden apartment’ is going to become a weird antique word, like ‘phonograph,’” said Dan Markson, senior vice president for The NRP Group, one of the nation’s largest affordable housing developers, based in Cleveland. His firm is building an increasing number of townhouses in its mix of affordable housing construction.

The Carpet Cottage takes the townhouse to even higher densities, but without a second floor. The architects at Duany Plater-Zyberk & Co. (DPZ) began with architect Marianne Cusato’s celebrated “Katrina Cottage” design for a small, inexpensive single-family house, which provided an alternative to the trailers the government provided to people left homeless by hurricanes Katrina and Rita.

DPZ has fit 14 of these small houses together into a cluster of one-story attached houses. The result is the Carpet Cottages—a design that could have a huge impact beyond the Gulf Coast in towns with a big need for housing but only small sites to develop and little appetite for tall buildings.

Developers can gather just five conventional lots measuring roughly 50 feet by 100 feet on a corner of a traditional city block, cut a new, L-shaped street to separate the corner from the rest of the block, and create a small block measuring just 207 feet by 87 feet. Residents can parallel park 22 cars on the streets that border the block.

The density of the Carpet Cottages on this lot would be high even for a typical, multi-story garden community. It works out to the equivalent of 35 units per acre, though the designer’s plan would only put 14 of the Carpet Cottages together at a time, mixing the sets of cottages in among conventional single-family homes.

These attached houses fill the lot, effectively creating a single, 14-unit building, though each house will have its own front door. Ten of the 14 cottages have two bedrooms and will measure a relatively generous 890 square feet. Five of these two-bedroom units will even have small private front yards. The cluster of houses also includes two smaller, one-bedroom, 682-square-foot units on the back corners of the lot and two larger homes with four bedrooms, two baths, and 1,082 square feet on the front corners of the lot.

These Carpet Cottages can be produced anywhere that local officials are willing to allow them. None have been built, yet, but there is interest. At Jackson Barracks, a National Guard base on the border between New Orleans’ ravaged Ninth Ward and St. Bernard Parish, Cypress Realty Partners is negotiating with officials to start construction this year on about 100 new rental cottages, including several sets of Carpet Cottages.

The hard cost to construct the Carpet Cottages at Jackson Barracks will average just $105 to $110 per square foot. That’s very competitive compared to the construction costs of traditional garden apartments, especially in Louisiana, where contractors and construction materials are scarce.

The biggest challenge to building Carpet Cottages will be gaining the trust of local officials, who must make room for the innovative new design in their zoning rules, which typically require more conventional construction, such as single-family homes on half-acre lots.