For many video compression systems, overlapped blocked motion compensation (OBMC) Provides an effective extension of tradition block MC (BMC). However, because OBMC causes noncausal special interaction between blocks, iterative methods have typically been used for motion estimation (ME) for OBCM. For compression purposes, the rate for the motion vector field may also be constrained. This paper considers several rate-constrained ME methods for OBMC. Experiments demonstrate that a simple rate-scan algorithm is effective as a suboptimal non-iterative solution, with better rate distortion performance and equal or lower computational complexity than several iterative methods.