Mining frequent patterns is a major topic in data mining research, resulting in many seminal papers and algorithms on item set and episode discovery. The combination of these, called composite episodes, has attracted far less attention in literature, however. The main reason is that the well-known frequent pattern explosion is far worse for composite episodes than it is for item sets or episodes. Yet, there are many applications where composite episodes are required, e.g., in developmental biology were sequences containing gene activity sets over time are analyzed. This paper introduces an effective algorithm for the discovery of a small, descriptive set of composite episodes. It builds on our earlier work employing MDL for finding such sets for item sets and episodes. This combination yields an optimization problem. For the best results the components descriptive power has to be balanced. Again, this problem is solved using MDL.