Both Kate’s husband and her closest female friend want to possess her and her past.

Obsessed with memories, the rivals have shaped recollections stressing their respective importance in Kate’s life. Whether their stories are even a little bit true is unclear, but in Harold Pinter’s enigmatic “Old Times,” now in production at Shakespeare Theatre Company, veracity takes a back seat to the power of relationships and the mistiness of memory.

Seated in the starkly white living room of their quiet seaside home, Deeley (Steven Culp), a successful filmmaker, and his beautiful wife Kate (Tracy Lynn Middendorf) discuss the imminent visit of Anna (Holly Twyford), an old friend whom Kate hasn’t seen in 20 years and her husband has never met. In fact, Deeley knows precious little about Anna, and the tidbits his wife has offered — that Anna is not only her oldest but also her only friend; that they were once flat mates in London; that she used to steal Kate’s underpants – have done nothing to endear her to him.

Anna arrives. Over drinks (and cigarettes), she and Deeley genteelly set to battle while Kate curled up on the couch like a cat looks on rather amusedly. Initially Anna – witty and sociable — recounts the fun times she and Kate shared as single young women in London. In reply, Deeley relays how he first met Kate at a grungy cinema where they’d both gone to see the aptly titled “Odd Man Out.” Anna remembers things differently. She says she saw the film with Kate but Deeley wasn’t there. Eventually, the conversation escalates into a heated contest of who knows Kate best. They even compete in singing the half-forgotten lyrics of Kate’s favorite old songs.

When Kate leaves the room to bathe, Deeley says he remembers Anna from their London days. He claims they drank at the same pub, and one night he even peeked up her skirt at a party. Initially Anna says it can’t be true, but then changes her tune, admitting she was at the party wearing Kate’s underwear. What to believe? At one point Anna says, “There are some things one remembers even though they may never have happened.”

While Deeley’s stories about Kate are tinged with sex (he tends to objectify her), Anna’s intimate moments/memories are more gentle — she strokes Kate’s arm while asking if she might draw her bath or read aloud to her. Anna now lives as expat with her husband in Sicily, or so she says. Here, very little is for certain. But clearly she was at one time — or still is — in love with Kate and Kate seems to respond positively to her expressions of tenderness. Feeling relegated to third wheel status, Deeley grows increasingly angry and is ultimately reduced to heaving sobs.

Impeccably staged by Shakepeare’s gay artistic director Michael Kahn, the production is taut and very funny. The three-person cast is first rate. Making her debut at Shakespeare, Twyford (who is also gay) handles the brief, precise Pinter dialogue beautifully, and rather hilariously fills the playwright’s well-known pauses with expectant frozen smiles.

Jane Greenwood’s costumes nicely illustrate Anna and Kate’s differences: In addition to a slick chignon, the former wears a rather severe dress with a bow at her throat while the latter’s casual peach clothes and loose-fitting pink robe describe a softer, less dramatic person. Deeley is appropriately tweedy as the accomplished documentarian relaxing away from town.

Walt Spangler’s bright white set makes a perfect blank slate on which to scribble and erase memories, real and imagined.