An earlier production of this clever musical was a Times Critic’s Pick two years ago when the show was burdened with the title “Who’s Your Baghdaddy Or How I Started the Iraq War.” Now it is playing at St. Luke’s Theatre. The location is appropriate, because the opening scene is set in a church basement. There’s free coffee and donuts onstage before the play as if we were gathered for an AA meeting. This support group, however, is not for alcoholics, but for the CIA operatives responsible for the Iraq War. Whether through stubbornness, careerism, delusion, error or deception, each has done something that leads to war. We also meet a junior agent in the German intelligence service, whose knowledge of Arabic leads to his being assigned to interrogating an Iraqi defector, code name “Curveball,” who claims he worked on building mobile labs for the manufacture of biological weapons back in Iraq. When the German agency seeks technical assistance from the CIA, complications multiply. The talented cast (Brennan Caldwell, Jason Collins, Bob D’Haene, Brandon Espinoza, Joe Joseph, Claire Neumann, Larisa Oleynik and Ethan Slater) perform with gusto. The music by Marshall Pailet (who also directs) is eclectic, the lyrics by A.D. Penedo are often clever, and the book by both of them, based on an unproduced screenplay by J.T. Allen, is almost consistently lively. The choreography by Misha Shields adds fun. The barebones set by Caite Hevner suits the production. My only quibble is that it could benefit from a slight trim. The play is certainly timely as the prospect of getting into a war by accident seems all too real. Running time: two hours, including intermission.