The lek paradox, in which female choice erodes genetic variation in male sexually selected traits, is a fundamental issue in sexual selection. If females gain only genetic benefits from preferentially having their ova fertilized by males with particular traits, what maintains variation in these traits? Under strong directional selection mediated through mate choice, the alleles for beneficial male traits are expected to go to fixation and exhibit little variation. A theoretical solution to the lek paradox is the genic capture hypothesis which states that: costly male traits subject to female choice are condition dependent, that male condition is dependent on genes at many loci and exhibits additive genetic variance, and that positive genetic correlations exist between sexually selected traits and condition. Using a captive population of the zebra finch Taeniopygia guttata, we tested two key predictions from this model: (1) that genetic variance exists in beak color which is a sexually selected trait, but also in condition and immune function, and (2) that positive genetic correlations exist between condition and beak color, and between beak color, condition, and immune function. Genetic parameters were estimated from a large breeding experiment involving 81 sires, 972 offspring, a pedigree of 1526 individuals, using the animal model. We employed the following index of body condition: residuals from a log-log plot of body mass on tarsus length following a standardized and extended period of exercise, in which residual mass is known to reflect fat and protein reserves. Our results were broadly consistent with the genic capture hypothesis because we found (1) additive genetic variation in beak color and immune function and condition, and (2) positive genetic correlations between condition and beak color, and between condition, beak color, and several assays of immune responsiveness. However, both of these results need qualification. In the first case we identified an important general problem in estimating the coefficient of additive genetic variance (CV_A) in body condition. In the second case, although most of the genetic correlations were positive as predicted, only some were statistically significant, possibly due to our relatively small sample sizes, because genetic correlations typically have large standard errors and therefore require very large samples to be statistically significant. The statistically significant, positive genetic correlations included those between beak color and immune function (response to tetanus), and between immune function (response to tetanus) and condition, both of which indicate that females gain good genes from mating with males in good condition and/or with a redder beak color. We discuss the implications of our results for devising more rigorous but pragmatic tests of the genic capture hypothesis.