Inferences about the evolution of continuous traits based on reconstruction of ancestral states have often been considered more error-prone than analysis of independent contrasts. Here we show that both methods in fact yield identical estimators for the correlation coefficient and regression gradient of correlated traits, indicating that reconstructed ancestral states are a valid source of information about correlated evolution. We show that the independent contrast associated with a pair of sibling nodes on a phylogenetic tree can be expressed in terms of the maximum likelihood ancestral state function at those nodes and their common parent. This expression gives rise to novel formulae for independent contrasts for any model of evolution admitting of a local likelihood function. We thus derive new formulae for independent contrasts applicable to traits evolving under directional drift, and use simulated data to show that these directional contrasts provide better estimates of evolutionary model parameters than standard independent contrasts, when traits in fact evolve with a directional tendency.