Characters in interactive 3D applications are often animated by creating transitions from one motion clip to another in response to user input. It is not trivial, however, to achieve quick, natural-looking transitions between two arbitrary motion clips, especially when the two motions are dissimilar. To tackle this problem, we present a simple framework called optimal one-hop motion transition, which creates quick, natural-looking transitions on the fly without requiring careful manual specifications. The key ideas are (1) to insert a short intermediate motion clip, called a hop, between the source and destination motion clips, and (2) to select such a hop motion clip and its temporal alignment in an optimal way by solving a search problem. In the search problem, our framework tries to balance the naturalness of the resulting transitions and the responsiveness to user input. This search can be precomputed and the results can be stored in a lookup table, making the runtime cost to play an optimal transition negligible. We demonstrate that our framework is easily integrated into a widely used game engine, and that it greatly improves the quality of transitions in practical scenarios.