The thriller spoof “The 39 Steps” milks absurdity for all it’s worth, the shtick involving a milkman being a case in point. A mere four actors depict dozens of spies, witnesses, police officers and other colorful characters in Patrick Barlow’s 2005 tongue-in-cheek play, now on view in an underwhelming and overlong Constellation Theatre Company production. The impracticality of the show’s role-juggling is part of the joke.

For example, when Christopher Walker plays a salt-of-the-earth London milkman, he can’t also shoulder the role of the lurking secret agent he depicted moments before. So when the secret agent needs to make another appearance in the same scene, the character’s hat — held up by another actor — stands in for the whole. Cue audience chortling.

Reveling in the limits of dramatic illusion, such gags are the soul of “39 Steps,” adapted from Alfred Hitchcock’s 1935 movie and John Buchan’s original 1915 novel. But pulling off this kind of funny business is tricky: A “39 Steps” production needs to suggest the arduousness of theatricality without making its theatricality feel arduous. Lickety-split pacing, razor-precise movement and superb comic timing are essential. As of opening night, the Constellation production, directed by Nick Olcott, rarely exhibited these qualities. Jokey stage business frequently dragged (a scene involving handcuffs was particularly tedious); actor physicality occasionally lacked sharpness; and the characterizations sometimes tended toward mugging, rather than the lightning-etched farcical portraits the play demands.

Admittedly, at the reviewed performance, gales of audience laughter erupted regularly at the escapades of Richard Hannay (a passable Drew Kopas), a 1930s Londoner inadvertently drawn into an international espionage plot. Fleeing both from villains and law enforcement, who suspect him in a murder, Hannay survives skulduggery in a vaudeville theater, a chase atop a speeding train and other cloak-and-dagger stuff.

Patricia Hurley does the most to energize the Constellation production, with crisp, funny impressions of Hannay’s love interests, such as an absurdly sultry femme fatale. Walker and Gwen Grastorf do a decent job channeling all the other personages, including innkeepers and traveling lingerie salesmen. Amid A.J. Guban’s film noir scenic design, Sabrina Mandell’s period costumes add further atmosphere.

But the production’s key asset — other than Hurley — is the shadow puppetry, which conjures a plane crash, glimpses of mysterious conspirators and more. (Alex Vernon is the puppet designer, and Guban devised the lighting.)

The artful shadow puppetry makes other production elements feel all the more workmanlike. A “39 Steps” should ascend the comic heights. This one too often hangs out on a landing.

The 39 Steps, adapted by Patrick Barlow from the Alfred Hitchcock movie and John Buchan novel. Directed by Nick Olcott; movement director, Mark Jaster; fight and intimacy director, Jenny Male; sound design, Gordon Nimmo-Smith; properties, Olcott, Allison Arkell Stockman, Nick Martin and Pamela Weiner. About 2 hours 10 minutes. $25-$45. Through March 8 at Source, 1835 14th St. NW. 202-204-7741. constellationtheatre.org.