Basic economic models adapted from foraging theory predict that decisions in mate choice may be determined either by ‘best-of-n’ preference functions or by sequential rules incorporating acceptance thresholds. However, in some species, more complex determinations that incorporate versions of both protocols are found. To understand the functions of co-occurring protocols, we studied mating decisions in the lesser wax moth, Achroia grisella (Lepidoptera: Pyralidae), an acoustic species in which females prefer males, the advertisement songs of which are delivered at relatively high ‘pulse-pair’ rates. In addition to this preference, A. grisella females avoid mating with a male, the song of which does not exceed a minimum pulse-pair rate, and they hold to this criterion even when no other singing males are present and regardless of song amplitude. Thus, mating decisions are not simply based on acoustic power (pulse-pair rate × amplitude). We recorded male songs and female responses in an A. grisella population and found that male pulse-pair rates showed a median of 87/s and ranged from 50 to 115/s, while female acceptance thresholds for male song showed a median of 60/s and ranged from 30 to 105/s. The distributions of thresholds were approximately normal and were not significantly skewed toward the right. Male song rates declined slightly with age, but female thresholds remained stable over the adult lifespan. Both the male and female traits showed significant repeatability within individuals. Whereas phylogenetic inference indicates that hearing in pyralid moths originated as a means of avoiding predation by insectivorous bats, the specific distribution of female acceptance thresholds suggests that currently this protocol does not primarily function to preclude inappropriate, and potentially lethal, responses to bat echolocations: pulse rates in the searching-phase echolocations used by either aerial-hawking or substrate-gleaning bats mostly range from 10 to 20/s, and the lack of positive skew in the distribution of thresholds indicates an absence of directional selection from the left. Rather, we infer that thresholds augment preference functions in A. grisella by precluding mating with males which are markedly inferior in a critical song character. In general, co-occurring protocols may be important where population density fluctuates markedly, as preference functions may be ineffective in preventing mating with inferior males when density is low.