Ross Destiche, left, and Ryan Tumulty in ”Equus.” (DJ Corey Photography/DJ Corey Photography)

A psychiatrist knows he has the skills to banish a troubled boy’s delusions, but will he also squelch his capacity for passion and wonder?

The question reverberates throughout Peter Shaffer’s groundbreaking 1973 play “Equus” and Constellation Theatre Company’s polished and perceptive revival, fluidly staged by Amber McGinnis Jackson.

The London-born Shaffer (“Amadeus,” “Lettice and Lovage,” “Black Comedy,” “The Royal Hunt of the Sun”) said he got the idea for “Equus” from a fragment of a story he had heard from a friend: A troubled teenager blinded a stable of horses with a spike. The playwright took that as his premise — a horrible crime committed by a seemingly gentle, lonely lad who, in Shaffer’s conceit, loves horses to the point of worship.

In the play, incomplete answers roll in as if out of a fog — a psychiatric mystery narrated by the attending physician and punctuated by halting revelations from the patient and his parents and flashbacks within flashbacks. The horses — in a piece of stagecraft that has always lifted this well-made piece out of the ordinary — are played by graceful actors wearing horses’ heads. Here, Mark Jaster has coached their proud and powerful, yet contained, movements.

The look of the production, starting with those horses’ heads, deserves special mention. Designed by Erik Teague, who also designed the costumes, the heads have a soft, slightly abstract shape, and they glow from within, their blank eyes and faces nearly white. The six actors wearing them are clad in light tones, too, their soft shoes enhanced with metal to make a clip-clop sound. A.J. Guban’s striking, uncluttered set, with its light walls and dark beams, recalls both suburban Tudor architecture and a barn. With the audience seated on two sides, it’s almost an operating theater. Guban also designed the lighting, which is gorgeous but never distracting.

Michael Kramer, as psychiatrist Martin Dysart, anchors the cast of skilled performers who are in tune with the slightly declamatory, confessional style of the piece and secure in a range of British accents. Kramer brings a rumpled authority and a little edge to Dysart, who accepts only grudgingly the case of young Alan Strang (Ross Destiche). Stuck in a job and a marriage that no longer give him joy, Dysart longs to renew his soul where his own passions lie: in the ruins of classical Greece.

The judge (Kathleen Akerley) in Alan’s case begs her old friend to take the boy on for evaluation and treatment. A moment with him persuades Dysart to accept: He’s a mystery waiting to be solved. Destiche literally shrinks into the role of Alan. He seems too big and adult at first but skillfully transforms into a smaller, more frail and childlike character.

Dysart gradually uncovers what happened that night in the stables, where Alan, an awkward and friendless 17-year-old, worked to muck out stalls and groom the creatures he loved, and where a pretty co-worker (an excellent Emily Kester) flirted with him. Ryan Tumulty cuts an impressive figure of contained power and grace as Alan’s favorite horse and, in more distant flashbacks, as the iconic horse of his fantasies.

Dysart excavates Alan’s formative years and collects from his contentious parents — a blustery atheist father (Michael Tolaydo) and a pious, Bible-quoting mother (Laureen E. Smith) — scraps of information that eventually form a map into Alan’s delusions.

It is Dysart’s envy of Alan’s private passion, however misshapen, that is playwright Shaffer’s refrain. Dysart longs to feel anything as strongly and fears he must destroy Alan in order to save him.

The doctor’s dilemma and that of his suffering young patient play out rivetingly in Constellation’s fine staging.

Equus, by Peter Shaffer. Directed by Amber McGinnis Jackson. Composer and sound designer, Palmer Hefferan. With Karina Hilleard, Colin Smith, Tori Bertocci, Gwen Grastorf, Ashley Ivey, Ryan Alan Jones and Emily Whitworth. About 2 1/2 hours. One scene contains full nudity. Produced by Constellation Theatre Company at Source Theatre, 1835 14th St. NW, through Feb. 14. Tickets: $23-$50. Call 202-204-7741 or visit constellationtheatre.org.