A passerby on 14th Street during the press-night intermission of Constellation Theatre’s rich and entrancing new production of Equus pointed to the poster and advised her friends that Peter Shaffer’s complex 1973 drama is “the one where Daniel Radcliffe fucks a horse.” Reductive, but not wrong. The actor who takes on the role of Equus’ horse-obsessed young subject, Alan Strang, is called upon to bare soul and body alike. Radcliffe, who played the role at 18 in a 2007 West End revival and then again on Broadway, was by most accounts tremendous.

The play is narrated by Martin Dysart, the psychiatrist overseeing Alan’s treatment at the residential facility to which he’s legally referred after taking a spike to six horses’ eyes—a grisly and cruel yet curiously specific act of violence. There are other characters, but we experience every scene from Dysart’s point of view. A clever device that Shaffer uses throughout is to have Dysart or Alan perform a scene with a third character on stage while simultaneously recounting the exchange in a therapy session later. In the steady hands of director Amber McGinnis Jackson, the tension and calibration of these scenes never comes at the expense of clarity.

As Alan, Ross Destiche radiates anger and a desperate need to be understood. Though he bares a passing resemblance to Radcliffe, his aquiline features more strongly suggest a young Willem Dafoe. Dysart is at least as daunting a role; like so many headshrinkers of stage and screen, he must show us how becoming emotionally entangled with a patient forces him to consider his own barren life. Michael Kramer makes you forget that this is always what happens to fictional psychiatrists.

Erik Teague’s costumes for the half-dozen actors playing the horses are otherworldly and almost comically simple—above, impressive horsehead helmet; below, sand-colored suede boots with horseshoe-shaped taps on the soles. The floorboards of A.J. Gruban’s striking wood-paneled set, which bisects the audience and serves adequately as both an office and a stable, tremble visibly and thunderously beneath their steps. Michael Tolaydo and Laureen E. Smith do sensitive work as Alan’s bewildered parents, as estranged from one another as they are from their fey son. Emily Kester is marvelous, too, as a peer of Alan’s who takes an interest, little suspecting how damaged the boy is.

Dysart’s concern that “curing” Alan of his pathology might consign him to a life without passion or color is also a theme of A Clockwork Orange. Anthony Burgess’ novel was published a decade before Shaffer’s play appeared, but Stanley Kubrick’s controversial film of Clockwork hadn’t come out until the end of 1971, less than two years before Equus. The protagonist of Burgess’ story is a rapist and pedophile without remorse; not a tortured kid who has harmed animals in a single, bizarre episode. But the troubling notion that free will comes at an occasionally horrific cost is present in both stories. That Equus gnaws at the bit of such pat explanations of the unknowable remains its most enduring virtue.

1835 14th St. NW. $20–$45. (202) 204-7741. constellationtheatre.org.