A fundamental and frequently overlooked aspect of animal learning is its reliance on compatibility between the learning rules used and the attentional and motivational mechanisms directing them to process the relevant data (called here data-acquisition mechanisms). We propose that this coordinated action, which may first appear fragile and error prone, is in fact extremely powerful, and critical for understanding cognitive evolution. Using basic examples from imprinting and associative learning, we argue that by coevolving to handle the natural distribution of data in the animal's environment, learning and data-acquisition mechanisms are tuned jointly so as to facilitate effective learning using relatively little memory and computation. We then suggest that this coevolutionary process offers a feasible path for the incremental evolution of complex cognitive systems, because it can greatly simplify learning. This is illustrated by considering how animals and humans can use these simple mechanisms to learn complex patterns and represent them in the brain.