Traditional video compression methods obtain a compact representation for image frames by computing coarse motion fields defined on patches of pixels called blocks, in order to compensate for the motion in the scene across frames. This piecewise constant approximation makes the motion field efficiently encodable, but it introduces block artifacts in the warped image frame. In this paper, we address the problem of estimating dense motion fields that, while accurately predicting one frame from a given reference frame by warping it with the field, are also compressible. We introduce a representation for motion fields based on wavelet bases, and approximate the compressibility of their coefficients with a piecewise smooth surrogate function that yields an objective function similar to classical optical flow formulations. We then show how to quantize and encode such coefficients with adaptive precision. We demonstrate the effectiveness of our approach by comparing its performance with a state-of-the-art wavelet video encoder. Experimental results on a number of standard flow and video datasets reveal that our method significantly outperforms both block-based and optical-flow-based motion compensation algorithms.