Genetic correlations between parasite resistance and other traits can act as an evolutionary constraint and prevent a population from evolving increased resistance. For example, previous studies have found negative genetic correlations between host resistance and life-history traits. In invertebrates, the level of resistance often depends on the combination of the host and parasite genotypes, and in this study, we have investigated whether such specific resistance also acts as an evolutionary constraint. We measured the resistance of different genotypes of the fruit fly Drosophila melanogaster to different genotypes of a naturally occurring pathogen, the sigma virus. Using a multitrait analysis, we examine whether genetic covariances alter the potential to select for general resistance against all of the different viral genotypes. We found large amounts of heritable variation in resistance, and evidence for specific interactions between host and parasite, but these interactions resulted in little constraint on Drosophila evolving greater resistance.