Have you ever wanted to be in two places at the same time? The characters do it in Tom Stoppard's 1988 "Hapgood," a very tricky play about love and spies during the Cold War.

At least the people appear to be in two places at once. Watch carefully as the shell game starts in the Washington Shakespeare Company's perceptive, if guarded, production at the Clark Street Playhouse: Stealthy figures come and go in the locker room of some sort of spa, casually sliding briefcases under changing cubicles and draping colored towels over railings as a kind of code. All the while, a man pretends to shave while monitoring every move in the mirror. On the walkie-talkies, everyone answers to someone named "Mother."

When it's over, even the experts aren't sure who was where and doing what. Stoppard being Stoppard, it's nothing that cannot be explained by a brief speech on particle physics, making it seem perfectly natural for something to be in two places at once, or not at all the thing you're looking at.

That explains the problem that flows from the baffling roundelay of briefcases, and it leads to a theatrically juicy solution, too, while making you regard several key relationships afresh along the way. The situation, in brief: The Brits are trying to pass the Russians some disinformation about the Strategic Defense Initiative, but something's gone wrong -- someone's playing both sides. Hapgood, the "Mother" who's running the operation, has to sort it all out. The suspects include a Russian scientist and double agent named Kerner, a hot-tempered English operative named Ridley and Hapgood herself.

No one does intellectual puzzlement better than Stoppard, and the deliberate mysteries of espionage suit him well. (So do the political and personal passions that give human shape to the maneuvers, although "Hapgood" moves with such dry speed, like a monorail, that they often seem like afterthoughts.) The language, by and large handled with skill by the WSC ensemble, is infused with a crisp British professionalism: "I'm here to be told," Hapgood murmurs into various communications devices, and as Kathleen Akerley says it -- coolly, as if it has been said a thousand times before -- the phrase has a delicious imminence. Things are happening, cryptic and momentous. There's no time for games.

Yet gamesmanship is what it's all about, and the twin challenges of "Hapgood" are to make it clear and to make it fun. Co-directors Christopher Henley and Alexandra Hoge are better at the former than the latter; their staging is cautious and oddly stationary. Actors stand still, as if to make sure we don't miss a trick of the dialogue, and although locations sometimes shift significantly, Elizabeth Jenkins McFadden's set doesn't metamorphose with much distinction. (Jason Arnold's perfunctory lighting design doesn't help.) The sluggish design hampers things a bit when "Hapgood" actually springs into action, offering more deceptions and revelations on the go.

But aside from Ian Armstrong's bellowing as an intelligence officer named Blair (whom Armstrong seems to think of as the town crier), the acting is sensible. Bruce Alan Rauscher, as the Russian scientist, brings lucidity and a touch of melancholy to the technical speeches, and Hugh T. Owen does deft, slippery work as Ridley, making clear that the character is as much a gangster as he is a spy. (He also has a more cogent grasp of Cold War politics than most of his colleagues.)

And Akerley, better known as a director with the Washington Shakespeare Company and with her own Longacre Lea company, is a fine centerpiece; she gives a restrained performance that nicely measures the smarts, charm, and personal hurt that come into play. Her tactics aren't bad for handling the high-minded tomfoolery Stoppard offers here: Think. Relax. Make it look easy.

Hapgood, by Tom Stoppard. Directed by Christopher Henley and Alexandra Hoge. Costumes, Melanie Clark; sound design, Erik Trester. With Theodore M. Snead, Jay Hardee, Michael Dove, Brandon Thane Wilson and Nick Scott. About 21/2 hours. Through Dec. 4 at the Clark Street Playhouse, 601 S. Clark St., Arlington. Call 800-494-8497 or visit www.washingtonshakespeare.org

Kathleen Akerley gives it her best shot in "Hapgood."