The Hamilton & Zuk hypothesis (Hamilton & Zuk 1982) was tested in the European minnow, Phoxinus phoxinus (L.), where the male breeding characters include tubercles, which are horny growths on the skin of the head, and a bright red abdomen. Two trematode parasite species, neither directly transmitted, were present: Diplostomum phoxini in the brains of 100% of the fish and Macrolecithus papilliger in the guts of 44%. The heterozygosity of the fish at 11 loci was determined. The number of M. papilliger was negatively related to redness and positively related to the size of tubercles. The number of D. phoxini was not related to redness but was also positively related to the size of tubercles. Heterozygosity was positively related to redness and negatively related to the size of tubercles. This is the first report of such inverse relationships with heterozygosity. The number of tubercles was positively related to the size and condition of a fish. We suggest that males unable to develop exaggerated characters to display to females, e.g. a bright red abdomen, have the alternative strategy of emphasizing weapons for use in male-male competition. This effect could explain other reported positive correlations between parasite burden and sexual display.