The occurrence of additive genetic variance (VA) for male sexual traits remains a major problem in evolutionary biology. Directional selection normally imposed by female choice is expected to reduce VA greatly, yet recent surveys indicate that a substantial amount remains in many species. We addressed this problem, also known as the 'lek paradox', in Achroia grisella (Lepidoptera: Pyralidae), an acoustic moth in which males advertise to females with a pulsed ultrasonic song. Using a standard half-sib/full-sib breeding design, we generated F1 progeny from whom we determined VA and genetic covariance (COVA) among seven traits: three song characters, an overall index of song attractiveness, nightly singing period, adult lifespan, and body mass at adult eclosion. Because A. grisella neither feed nor drink as adults, the last trait, eclosion body mass, is considered a measure of 'condition'. We found significant levels of VA and narrow-sense heritabilities (h2) for all seven traits and significant genetic correlations (= COVAi,j / radical (VA i x VA j)) between most pairs of traits (i, j). Male attractiveness was positively correlated with body mass (condition), adult lifespan, and nightly singing period, which we interpret as an energy constraint preventing males in poor condition from singing attractively, from singing many hours per night, and from surviving an extended lifespan. The positive genetic correlation (r = 0.79) between condition and attractiveness, combined with significant levels of VA for both traits, indicates that much of the variation in male song can be explained by VA for condition. Finally, we discuss the morphological and physiological links between condition and song attractiveness, and the ultimate factors that may maintain VA for condition.