This paper addresses the problem of adapting overlapped block motion compensation (OBMC) windows for use with variable blocksize motion estimates. We tackle the problem by using a parametric window design, which expresses, based on a statistical motion model, the optimal weights as a function of the distances between the predicted pixel and its nearby block centers. The formula enables both prediction weights and prediction order to be adapted on a pixel-by-pixel basis. Extensive experiments have been conducted using JM 12.4. Compared with conventional block motion compensation, our scheme shows a bitrate saving of 18% (5% on average) while maintaining the same or even higher PSNR (0.1dB). It also provides a competitive advantage to variable block size motion compensation. Additionally, a hybrid of the two techniques achieves a further bitrate reduction of 13%. The result, nevertheless, provides only a lower bound on what is achievable since both motion estimation and mode decision were accomplished without considering OBMC. Further improvement is expected by incorporating iterative methods.