Variance components of sperm production traits (volume in ml, V; concentration in ×10⁶ sperm/ml, CN; sperm production in ×10⁶ sperm, PROD) were estimated in a paternal line of rabbit selected for 25 generations based on daily weight gain (DG, g/day) between 28 and 63 days of age. Features of the marginal posterior distributions for ratios of genetic variance, variance owing to non-additive plus environmental permanent male effects and variance owing to common litter of birth effects with respect to phenotypic variance are reported. The correlations between sperm production traits and the selection criteria were also estimated. Three sets of two-trait analyses were performed, involving 12908 records of DG, 2329 ejaculates corresponding to 412 bucks and 14700 animals in pedigree file. The heritabilities (h²) of the semen traits were 0.13 ± 0.05, 0.08 ± 0.04 and 0.07 ± 0.03 for V, CN and PROD, respectively. The permanent environmental effects were lower than the corresponding values of h² and varied between 0.06 and 0.11. A favourable and moderate genetic correlation was observed between V and DG (0.36 ± 0.34; p > 0: 0.83), together with a non-favourable and moderate correlation between permanent environmental effects owing to common litter of birth for both traits (-0.35 ± 0.35; p < 0: 0.85). On the other hand, the correlation between male permanent environmental effects for semen traits and DG was moderate and non-favourable (-0.51 ± 0.29 with p < 0: 0.95 for DG-CN, and -0.31 ± 0.37 with p < 0: 0.79 for DG-PROD).