By sheer necessity, the people who have run the Miami Rescue Mission in its 90 years of existence grew adept at squeezing a dollar to feed, house and rehabilitate innumerable homeless men, women and children.

More recently, they have developed something else as well: a knack for integrating inexpensive but distinctive design into its facilities as it gradually expands to meet the needs of its growing clientele.

The newest exhibit is an old warehouse behind the mission’s men’s center in Wynwood that’s being fully retrofitted to sleep 78 men in a dorm-like setting, complete with private lockers, study lounges and an auditorium with exposed rafters. Over the building front will go a swoopy canopy, and over the front door a MiMo-style half-moon eyebrow on which will stand letters spelling out the institution’s name in blue.

The new center, now under construction, was designed in efficient, simple-cool style by Miami architect Kobi Karp, best known for glitzy condo towers and hotels here and abroad, and it’s being built out by contractor and South Beach events promoter Michael Capponi, a longtime Rescue Mission supporter. Karp, Capponi and his subcontractors are all working for cost.

The Rev. Ron Brummitt, the Rescue Mission president, says the homeless deserve appealing surroundings as much as anyone else. The new building will be reserved for men enrolled in the mission’s transitional program, which has enjoyed a high rate of success setting homeless people on a path to jobs, homes and new lives through treatment, education and training.

“The main thing is, that building will give us extended ability to care for the homeless,’’ Brummitt said. “But we’re trying to modernize the space so it’s not sardine-ish, to make it comfortable. It will be a nice respite for these men.’’

Brummitt credits Capponi for undertaking the job and corralling Karp and a series of subs to work at a substantial discount.

“I couldn’t afford Kobi Karp,’’ Brummitt said with a laugh. “This man is known internationally.’’

The men’s dorm expansion comes 10 years after the Rescue Mission, which relies mostly on private donations, inaugurated its cornerstone community center, which features a stunning, natural-light basketball court and a soaring, multi-hued lobby. The community center was designed, also using low-cost, durable materials, by architect Marilyn Avery and the late William Lam, a famed pioneer in the field of architectural lighting design who was also responsible for the lighting of the Washington, D.C., Metro.

It has since become the site of the Miami Heat’s annual Thanksgiving giveaway, as well as after-school programs and sports leagues for kids from the surrounding neighborhoods, which include Wynwood and Overtown. On Wednesday, LeBron James, Dwyane Wade and their teammates handed out turkeys to local families at the center.

The expansion, which should be done in January, also coincides with the fast-moving transformation of the Wynwood warehouse district around the mission into a hip arts and entertainment magnet defined by a plethora of graffiti-art murals. When the mission moved into the neighborhood after relocating from downtown Miami in the 1980s, though, it was a desolate area of shuttered warehouses and vacant lots. The Rescue Mission built a new multi-story men’s center in 1989 at 2159 NW First Court, and also runs a shelter for women and children and a thrift store up the block.