Cognitive flexibility controls how animals respond to changing environmental conditions. Individuals within species vary considerably in cognitive flexibility but the micro-evolutionary potential in animal populations remains enigmatic. One prerequisite for cognitive flexibility to be able to evolve is consistent and heritable among-individual variation. Here we determine the repeatability and heritability of cognitive flexibility among great tits (
Parus major
) by performing an artificial selection experiment on reversal learning performance using a spatial learning paradigm over three generations. We found low, yet significant, repeatability (
R
= 0.15) of reversal learning performance. Our artificial selection experiment showed no evidence for narrow-sense heritability of associative or reversal learning, while we confirmed the heritability of exploratory behaviour. We observed a phenotypic, but no genetic, correlation between associative and reversal learning, showing the importance of prior information on reversal learning. We found no correlation between cognitive and personality traits. Our findings emphasize that cognitive flexibility is a multi-faceted trait that is affected by memory and prior experience, making it challenging to retrieve reliable values of temporal consistency and assess the contribution of additive genetic variation. Future studies need to identify what cognitive components underlie variation in reversal learning and study their between-individual and additive genetic components.