Multi-hypothesis prediction extends motion compensation with one prediction signal to the linear superposition of several motion-compensated prediction signals. These motion-compensated prediction signals are referenced by motion vectors and picture reference parameters. This paper proposes a state-of-the-art video codec based on the ITU-T Recommendation H.263 that incorporates multi-hypothesis motion-compensated prediction. In contrast to B-Frames, reference pictures are always previously decoded pictures. It is demonstrated that two hypotheses are efficient for practical video compression algorithms. In addition, it is shown that multi-hypothesis motion-compensated prediction and variable block size prediction can be combined to improve the overall coding gain. The encoder utilizes rate-constrained coder control including rate-constrained multi-hypothesis motion estimation. The advanced 4-hypothesis codec improves coding efficiency up to 1.8 dB when compared to the advanced prediction codec with ten reference frames for the set of investigated test sequences.