Key life history traits such as breeding time and clutch size are frequently both heritable and under directional selection, yet many studies fail to document micro-evolutionary responses. One general explanation is that selection estimates are biased by the omission of correlated traits that have causal effects on fitness, but few valid tests of this exist. Here we show, using a quantitative genetic framework and six decades of life-history data on two free-living populations of great tits Parus major, that selection estimates for egg-laying date and clutch size are relatively unbiased. Predicted responses to selection based on the Robertson-Price Identity were similar to those based on the multivariate breeder's equation, indicating that unmeasured covarying traits were not missing from the analysis. Changing patterns of phenotypic selection on these traits (for laying date, linked to climate change) therefore reflect changing selection on breeding values, and genetic constraints appear not to limit their independent evolution. Quantitative genetic analysis of correlational data from pedigreed populations can be a valuable complement to experimental approaches to help identify whether apparent associations between traits and fitness are biased by missing traits, and to parse the roles of direct versus indirect selection across a range of environments.