There is considerable disagreement over whether or not gaining viability benefits to offspring could be substantial enough to overcome the costs of female choosiness. A recent review suggested that the ‘lek paradox’ might be resolved by large indirect benefits as indicated by highly heritable ornamental traits. We selected males of a wolf spider Hygrolycosa rubrofasciata in relation to their sexual signalling rate (audible drumming). The estimated correlated response in offspring viability was rather small (0.12 s.d.). However, it may be large enough if the costs of being choosy are small. In fact, females mate with better–than–average males just by responding passively to a random drumming signal, and the active choice by females seemed to increase this benefit only slightly. In many mating systems, females obtain better–than–average males as a consequence of intense male–male competition or because of the extraordinary variance in male signalling. The costs of any additional choice may be so minor that female choice for honestly signalling males may evolve even with minute benefits in offspring viability. This may be the general solution to the lek paradox, as most studies report no apparent fitness benefits. Publication bias favouring statistically significant results may have led to an overemphasis on the few studies with large effects.