Fish are a rich source of omega-3 polyunsaturated fatty acids (n-3 PUFAs) and thus, they should be an integral part of human diet at least twice a week. As a result, high attention has been devoted to the improvement of fatty acids (FA) content in the flesh of farmed fish through nutrition. Conversely, there are very few data on the potential of selective breeding to improve FA composition in fish. We estimated genetic parameters of fillet fatty acid content and performance traits in market size common carp cultured under semi-intensive pond conditions. The experimental stock arose through factorial mating of 7 dams and 36 sires. All families were reared communally. Pedigree was reconstructed with microsatellite markers, and 158 individuals were dressed out and selected for flesh FA composition analysis. Heritability estimates of total muscle fat, FA composition in total fat (TF) (n-3 PUFA-TF, PUFA-TF, EPA-TF - eicosapentaenoic acid, n-6/n-3 - omega6/omega3 PUFA ratio), and most performance traits were moderately heritable (h(2) = 0.23-0.41), and body weight was highly heritable (h(2) = 0.62 +/- 0.20). Genetic correlations show that selection for faster growth would indirectly lead to fillet yield improvement (r(g) = 0.50-0.62) while having little impact on muscle fat (r(g) = 0.21). However, lipid quality in flesh would be affected: n-3 PUFA-TF would decrease and the n-6/n-3 PUFA ratio would increase. A likely interpretation is that faster growing genotypes consume more supplemental feed, which was poor in the beneficial FAs. For sustainable selective breeding, supplemental feed composition should be modified, so that faster growing carps would maintain an appropriate flesh quality.