The album was produced by Jay Beckenstein.[3] The band recorded the songs in less than a week, but spent two months in total working on Three Wishes.[4][5] There was more of an effort to record live in studio, after Beckenstein heard comments praising the band's live show over its albums.[6] Beckenstein also considered the songs on Three Wishes to be more thematically linked to each other rather than merely a collection of whatever songs the band had worked up.[7] "Jennifer's Lullaby" is dedicated to Stan Getz.[8]
The Washington Post deemed the album "a good deal less predictable and glossy than usual."[11] The Toronto Star wrote that "the veteran group is inoffensively competent, swings lightly despite the ugly rock 'n' roll drumming but contains about as much inspiration as a night watching Valium-powered TV soaps."[12]The Indianapolis Star determined that Three Wishes "is far more orchestrated than improvised, yet that keeps and perhaps deepens its entertainment edge."[10]