Many characteristics of organisms in free-living populations appear to be under directional selection, possess additive genetic variance, and yet show no evolutionary response to selection. Avian breeding time and clutch size are often-cited examples of such characters. We report analyses of inheritance of, and selection on, these traits in a long-term study of a wild population of the collared flycatcher Ficedula albicollis. We used mixed model analysis with REML estimation ("animal models") to make full use of the information in complex multigenerational pedigrees. Heritability of laying date, but not clutch size, was lower than that estimated previously using parent-offspring regressions, although for both traits there was evidence of substantial additive genetic variance (h2 = 0.19 and 0.29, respectively). Laying date and clutch size were negatively genetically correlated (rA = -0.41 +/- 0.09), implying that selection on one of the traits would cause a correlated response in the other, but there was little evidence to suggest that evolution of either trait would be constrained by correlations with other phenotypic characters. Analysis of selection on these traits in females revealed consistent strong directional fecundity selection for earlier breeding at the level of the phenotype (beta = -0.28 +/- 0.03), but little evidence for stabilising selection on breeding time. We found no evidence that clutch size was independently under selection. Analysis of fecundity selection on breeding values for laying date, estimated from an animal model, indicated that selection acts directly on additive genetic variance underlying breeding time (beta = -0.20 +/- 0.04), but not on clutch size (beta = 0.03 +/- 0.05). In contrast, selection on laying date via adult female survival fluctuated in sign between years, and was opposite in sign for selection on phenotypes (negative) and breeding values (positive). Our data thus suggest that any evolutionary response to selection on laying date is partially constrained by underlying life-history trade-offs, and illustrate the difficulties in using purely phenotypic measures and incomplete fitness estimates to assess evolution of life-history trade-offs. We discuss some of the difficulties associated with understanding the evolution of laying date and clutch size in natural populations.