“Village Wooing” defies all known laws of human behavior, but Rana Kay, left, and Michael Glenn manage to enrich their well-gauged comic portraits with glimmers of soul. (C. Stanley Photography/Washington Stage Guild)

Henry Higgins and Eliza Doolittle. Captain Bluntschli and Raina Petkoff. Napoleon and the Strange Lady in “The Man of Destiny.” Some divertingly incongruous duos gravitate toward each other in the plays of George Bernard Shaw, who in some alternate universe might well run a contrarian dating Web site (“Conversation, but no satisfaction, guaranteed”). Include in the list of odd couples: A and Z, the socially mismatched protagonists of “Village Wooing,” a 1933 playlet that’s slinging Shawian wit — and exhibiting a hint of romantic charm — courtesy of able performers Michael Glenn and Rana Kay.

Directed by Laura Giannarelli, “Village Wooing” is the watchable half of “Wives & Wits,” a Washington Stage Guild production that yokes together two love-themed one-acts by Shaw, the company’s most-favored playwright. When we meet A and Z, they’re strangers seated next to each other on a ship cruising the Red Sea. Comfortably ensconced in a deck chair, the seemingly ditzy Z (Kay) — a shop assistant blowing her savings on travel — is in a chatty mood. Her garrulousness irks A (Glenn), a snobbish, self-absorbed guidebook writer who is bent on penning 500 words before lunch. Flash-forward to a chance meeting between the two in an English village some months later: As A and Z trade quips about matrimony, rural life and the impact of capitalism on the social fabric, their relationship gradually shifts gears.

Overall, the plot line of “Village Wooing” defies all known laws of human behavior, but Kay and Glenn manage to enrich their well-gauged comic portraits with glimmers of soul: Check out the sly-but-patient half smile on Z’s lips as she trots about her shop, filling A’s orders for cheddar and ginger beer. (“Wives & Wits” set designer Jonathan Rushbrook created the store, whose front counter is crammed with almanacs, sugared almonds and other must-haves.) Or consider the moment when A puts his notebook down and seems to see Z for the first time, after she makes an inadvertent pun that makes him laugh. Even as they track the characters’ evolving rapport, the actors keep the verbal sallies flying at a satisfying pace.

Unfortunately, “Village Wooing” is the second piece on the “Wives & Wits” bill; the opener is director Alan Wade’s exasperatingly stagy version of Shaw’s 1912 comedy “Overruled,” about two genteel married couples who turn out to have quixotic views on honor and fidelity. When the strenuously flirting Gregory Lunn (Nick DePinto) and Mrs. Juno (Kay) discover a parallel dalliance between their respective spouses, Mrs. Lunn (Dawn Thomas) and Sibthorpe Juno (Glenn), the lounge of a seaside hotel erupts in repartee. (“I may be doing wrong; but I’m doing it in a proper and customary manner,” Mr. Juno gripes to Mrs. Lunn at one point. “You may be doing right; but you’re doing it in an unusual and questionable manner.”)

Moving around the red sofa and lace-draped stools of Rushbrook’s set, Kay’s Mrs. Juno displays some enjoyable poutiness, and Glenn’s Mr. Juno segues evenly from plummy leering to red-faced indignation. But, in general, the actors seem to be straining too hard for brittle Edwardian manners (DePinto seems particularly forced), with the result that the play feels as stiff and creaky as a loose drawing-room floorboard beneath a butler’s polished shoe. At least there are Lynn Steinmetz’s “Downton Abbey”-worthy costumes to admire while you wait for the intermission and for “Village Wooing” to begin.

Wren is a freelance writer.

Wives & Wits

Two one-act plays by George Bernard Shaw. Directed by Alan Wade and Laura Giannarelli; lighting, Marianne Meadows; sound, Marcus Darnley. About 2 hours 10 minutes. Through May 20 at the Undercroft Theatre of Mount Vernon Place United Methodist Church, 900 Massachusetts Ave. NW. Call 240-582-0050 or visit www.stageguild.org.