We present an approach to explanation in case-based reasoning (CBR) based on demand-driven (or lazy) discovery of explanation rules for CBR solutions. The explanation rules discovered in our approach resemble the classification rules traditionally targeted by rule learning algorithms, and the learning process is adapted from one such algorithm (PRISM). The explanation rule learned for a CBR solution is required to cover both the target problem and the most similar case, and is used together with the most similar case to explain the solution, thus integrating two approaches to explanation traditionally associated with different reasoning modalities. We also show how the approach can be generalized to enable the discovery of explanation rules for CBR solutions based on k-NN. Evaluation of the approach on a variety of classification tasks demonstrates its ability to provide easily understandable explanations by exploiting the generalizing power of rule learning, while maintaining the benefits of CBR as the problem-solving method.