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Females of many social Hymenoptera commit their reproductive potential to a single male; they mate once and never re-mate. Sexual selection theory predicts that under this regimen female precopulatory mate choice is crucial. The targets of female choice, male secondary sexual traits, should convey information about the functional fertility of the male. Here, we evaluated semen quality and its correlates in the paper wasp Polistes dominula , a monandric species with a lek-based mating system. The main goal of the study was to test whether sperm viability and the total number of sperm covaried with sexually dimorphic abdominal spots, body size and parasitic infection by Xenos vesparum. Surprisingly, superior male fertility was not predicted by attractive sexual traits, such as little round spots and large body size. We also found no effect of the parasite on male fertility, sexual ornamentation or body size. We found only that sperm viability was positively associated with the number of sperm. Moreover, there was evidence of a counterintuitive relationship between (sexually unattractive) large irregular spots and large body size of dominant successful males. Overall, our results suggest a condition-dependent trade-off between body size and costly sexual signals. [ABSTRACT FROM AUTHOR]