THE LUCY SHOW is a strange sort of band name, so it ought to follow that the music played by such a group would be equally odd. Yet there's nothing odd about the The Lucy Show's sound, an attractively melancholy approach to melody that fits somewhere between REM's folkish drones and Echo and the Bunnymen's moody psychedelia.

Neither Mark Bandola nor Rob Vandeven, The Lucy Show's two singers, seem to dwell much on the brighter side of life or love. But that hardly prevents " . . . Undone," the group's American debut, from exerting a powerful pull.

Part of the album's charm is the way producer Steve Lovell layers the instrumental textures, deftly applying feedback and reverb to thicken the sound without cluttering it. Some of the drama derives from studio add- ons -- a touch of viola to lighten "Resistance," keeping its rhythmic juggernaut from overpowering the vocal; cranking, moaning sound effects to deepen the sense of dread that pervades "Dream Days." But for the most part, it's the band's ability to embed melodic ideas deep within each arrangement that makes the romantic regret beneath the likes of "Remain" or "Ephemeral (This Is No Heaven)" so hauntingly real.

Like The Lucy Show, Marti Jones often sings of unhappy love, but that doesn't put a damper on the upbeat energy of "Unsophisticated Time," her solo debut. Although Jones is a relative newcomer -- her best-known band was the unjustly overlooked Color Me Gone -- she sings with great heart and impressive authority. It might have helped had the material been more even, but the few gems here, particularly "Lonely Is (As Lonely Does)," shine brightly.

THE LUCY SHOW -- " . . . Undone" (A&M SP-5088). MARTI JONES -- "Unsophisticated Time" (A&M SP- 5086); both appearing Saturday at the 9:30 Club.