The cast from “code name: CYNTHIA” with Axle Burtness, Zach Brewster-Geisz, Beth Amann, Christie Jackson, Will Hawkins. (Teresa Castracane )

About halfway through the World War II spy musical “Code Name: Cynthia,” a Washington society beauty preps for a heist. Under the eagle eye of an Allied intelligence mastermind, Betty Thorpe rehearses each step of the planned operation, coordinating with her unlikely mates — one a felon recently sprung from prison. As the music scales up and down in pitch, Betty and her teammates flub the procedure. They practice it again, and they flub again. And again. But each time, they get a little closer to mastery.

It was shrewd of book writer and lyricist Steve Multer and composer Karen Multer to build this sequence into their diverting and solidly crafted show, which is on view in a gutsy, if ­under-resourced, world premiere production mounted by Pallas Theatre Collective at the Anacostia Arts Center. With its depiction of mishaps, the heist-rehearsing number, “The (More or Less) Perfect Plan,” helps ground a story whose romance, glamour and high-stakes suspense seem like gifts from the espionage-tale gods.

Despite its storybook qualities, Betty Thorpe’s story is a true one. (A visit to Washington’s International Spy Museum brought it to the Multers’ attention). As told in “Code Name: Cynthia,” Betty (Gracie Jones) is a determined young woman who spies for the Allies in Europe, escaping as Paris falls to the Germans. Returning to Washington, where her mother, Cora Wells (Karen Lange), is a society hostess, Betty resolves to live a quiet life with Arthur Pack (Joshua Simon), the British diplomat who she is about to marry. But those plans change after Canadian intelligence operative William Stephenson (Jason Hentrich) blackmails her into resuming her spy career — this time, in Washington.

The Multers have packed this Alan Furst-meets-“The Americans” plotline into a tight, effective musical, complete with a satisfying narrative twist near the end. Confidently portrayed by Jones in the Pallas Theatre production, which is directed by Tracey Elaine Chessum, Betty comes across as a compelling figure: She’s rebellious, idealistic and courageous, yet she longs, a little ambivalently, for security. The story’s supporting characters are mostly colorful and sturdy, although Charles Brousse (Chris Oechsel), the press attache at the embassy of Vichy France, who becomes one of Betty’s conquests, seems something of a Gallic cartoon.

The saga gains added heart and seriousness from scenes that explore the situation of Betty’s ­isolationism-advocating mother, whose relationship with Betty is tense. Both women feel utterly at home in Washington’s social-political industrial complex, which itself becomes a character in the story, starting with the jaunty number “Somewhere in Washington” (“Somewhere in Washington/ Graft and vice fall into bed/ Edward Murrow shakes his head”). This song, like others in the show, combines catchy hooks with music that seems to embody the nervous energy of the World War II world.

Gracie Jones as the title character in “code name: CYNTHIA” by Pallas Theatre. (Teresa Castracane)

International intrigue, D.C. landmarks, cloak-and-dagger shenanigans — that’s a lot to evoke in a black-box-theater staging. This edition of “Code Name: Cynthia” very much has the feel of a placeholder for a future, better-funded production. With the exception of Russell Silber, who adeptly channels the tale’s ace-safecracker character, the Georgia Cracker, few of the performers have as much stage presence as Jones.

The supporting players and ensemble often look hesitant, as though they hadn’t benefited from enough rehearsal time. The tentativeness in performance can make some of the script’s more trite turns of phrase (“Honesty doesn’t win wars; intelligence does”) feel all the more prepackaged. And, apart from Betty’s elegant garb, the costumes look ill-fitting.

On a more positive note, the show’s projections (including photos, maps and building plans) suggest the story’s scope while allowing for rapid scene changes. (Chessum and Caroline Brent devised the multimedia design). One projection rounds out the narrative with a denouement that will warm the heart of every romantic.

“Code Name: Cynthia.” Book and lyrics, Steve Multer; music, Karen Multer. Directed by Tracey Elaine Chessum; music direction, Amy Conley; orchestration, Scott AuCoin; costume design, Brian J. Shaw; lighting, Jason Aufdem-Brinke; choreography, Michael J. Brown; fight choreography, Chris Niebling. With Beth Amann, Zach Brewster-Geisz, Axle Burtness, Will Hawkins, Christie Jackson and Kathleen Mason. About 2 hours and 20 minutes. Through Aug. 16 at Anacostia Arts Center, 1231 Good Hope Road, SE. Tickets: $15-$25.

Wren is a freelance writer.