“Perfect Arrangement” starts off like a zany sitcom from the 1950s. But as the comedy plays out, things become less “I Love Lucy” and more “Dragnet,” if that show were about hunting undesirables in the U.S. government during the McCarthy era.

That’s the sword of Damocles hanging over two couples living side by side in a Georgetown duplex. Bob Martindale (Matthew Stuart Jackson) works for the State Department, combing through the ranks and weeding out “drunkards, loose women and deviants.” And by deviants, the government means gays. He and his wife, Millie (Erynn Dalton), are best friends with next-door neighbors Jim Baxter (Daniel Capote) and his wife, Norma (Arlette Del Toro), who is also Bob’s secretary.

Playwright Topher Payne has also mixed in dialogue that mimics TV commercials. Giddy references to biscuit mix, furniture polish and hand cream keep popping into the action. He maintains that TV gloss and ol’ switcheroo plot device effectively, even when the situation-comedy brassiness begins to evaporate as the Red Scare devolves into the Lavender Scare for the Martindales and the Baxters.

The cast is deliciously good, especially Ostrenko, Groom and Dalton. They wield the words well, even if a few opportunities for even wackier physical humor pass by unexploited as Payne and director Andy Rogow seem eager to tackle the more serious stuff. The costumes, a perfect parody of 1950s fashion, almost steal the show, increasingly festooned with geegaws by designer Peter A. Lovello until they appear almost Seussical in the second act. Sure, the ending feels too tidy and didactic by far, but in the current political climate, “Perfect Arrangement” still manages to fairly vibrate with relevancy.

“Perfect Arrangement” runs through Dec. 11 at Island City Stage, 2304 N. Dixie Highway, in Wilton Manors. Showtimes are 8 p.m. Thursdays-Saturdays and 5 p.m. Sundays. Tickets cost $35. To order, call 954-519-2533 or go to IslandCityStage.org.