We give an optimisation for active learning algorithms, applicable to learning Moore machines with decomposable outputs. These machines can be decomposed themselves by projecting on each output. This results in smaller components that can then be learnt with fewer queries. We give experimental evidence that this is a useful technique which can reduce the number of queries substantially. Only in some cases the performance is worsened by the slight overhead. Compositional methods are widely used throughout engineering, and the decomposition presented in this article promises to be particularly interesting for learning hardware systems.