The trippy new drama “Goldfish Thinking” opens with bodies on the floor and a detective inspecting the wreckage. Clues: pay attention to them. Try to keep up. By the end of this cheerfully intricate brainteaser, you may still be wondering what exactly happened.

“The brain is not a simple place,” a law student named Warner murmurs to his dream-addled friend Dana. As this innocent-sounding line is dropped, the play shifts into a more daunting gear, leading its characters toward the tightest corners of a psychological maze.

Dana and Warner are part of a quartet of perky law student friends; when we meet them, they’re ignoring their case studies and doing Mad Libs. But Dana’s dark dreams give the gang a deeper puzzle to solve. Is someone dead? Did Dana commit a murder?

“Goldfish Thinking” is this year’s project from writer-director Kathleen Akerley’s Longacre Lea, a shoestring troupe with a tradition of producing just one show a year at the end of summer. (The venue: the small Callan Theatre at Catholic University.) Not all of Longacre’s shows are Akerley plays, but the ones that are have a British tang, influenced by the Harold Pinter and Tom Stoppard dramas that have attracted Akerley as a director, and sometimes as an actor.

Akerley’s “Goldfish” script sports more Stoppard fizz than Pinter menace, particularly as Heather Haney and Michael Glenn, playing Dana and Warner, banter about how to interpret Dana’s elaborate, mildly disturbing dreams. Haney generally puts a pleasant face on the inquiry; there is a tantalizing moment in the second act when she flickers with real panic, but it passes quickly. Haney’s Dana is mainly obsessively curious, not stricken.

Glenn is terrific at being casual or formal, easily managing both approaches within the same scene, and even more than Haney he keeps things playful. That’s helpful as the jokey-then-sober Warner and earnest Dana bring the audience along with their post-dream theorizing.

The dreams: that’s the other part of the show, and Akerley the director (assisted by Tom Carman) takes an effectively economical approach to getting us inside Dana’s twisted mind. A law professor without his pants, a droll Chairman Mao, a creepy woman clambering around on the floor in a way that makes it seem like her joints are attached all wrong: Akerley lets the actors construct most of the weirdness, with understated help from Elizabeth Jenkins McFadden’s jumbo law book set and Neil McFadden’s surreal soundscape.

Remarkably, the performers create this mental mayhem in a low-key but intriguing way. The ensemble for this tricky play is not as balanced as it might be, which sometimes breaks the mood (conversational one moment, slightly phantasmagorical the next). Still, especially nifty impressions are made by Chris Davenport tripling as Mao, a therapist, and a Brit named Basil, and by Slice Hicks as a deadpan dead man.

These figures are all in Dana’s head, which increasingly seems like a dangerous place to be. The show’s sudden ending may give you a “Wait . . . what?” moment; at times “Goldfish Thinking” is too true to the impenetrability of dreams. But a play that references Terry Gilliam’s dense and fantastical “Brazil” knows it’s leading you down a cult-y rabbit hole. Ye brave ones, dive in.

Goldfish Thinking

written and directed by Kathleen Akerley. Costumes, Gail Stewart Beach; lights, John Burkland. With Anna Brungardt, William Hayes, Ashley DeMain, Tyler Herman, Jennifer Hopkins and Jesse Terrill. About two hours. Through Sept. 9 at Callan Theatre, Catholic University, 3801 Harewood Rd. NE. Call 202-460-2188 or visit