The most straightforward approach in obtaining a down-converted image sequence is to decimate each frame after it has been fully decoded. To reduce memory requirements and other costs incurred by this approach, a down-conversion decoder would perform a decimation within the decoding loop. In this way, predictions are made from a low-resolution reference which has experienced considerable loss of information. Additionally, the predictions must be made from a set of motion vectors which correspond to the full-resolution image sequence. Given these conditions, it is desirable to optimize the performance of the motion compensation process. In this paper we show that the optimal set of filters for performing the low-resolution motion compensation is dependent on the choice of down-conversion filter. The motion compensation filters are determined as the optimal solution of a least squares problem. This problem is formulated in the context of two general classes of down-conversion techniques: one which is dependent on a single block, and another which is dependent on multiple blocks. General solutions for each class of down-conversion are provided. To demonstrate the usefulness of these results, a sample set of motion compensation filters for each class of down-conversion is calculated, and the results are incorporated into a low-resolution decoder. In comparison to a sub-optimal motion compensation scheme, the optimal motion compensation filters realize a drastic reduction in the amount of drift. Simulation results also reveal that the filters which were based on multiple block down-conversion can reduce the amount of prediction drift found in the single block down-conversion by as much as 35%.