In this paper, extrapolation of data in three dimensions is done in two steps. First, a three-dimensional annihilation filter is calculated from the available data. Next, the result of filtering an extended volume with the calculated annihilation filter from the first step is then minimized by computing the missing data in the extended volume. This technique suffers from a limited extrapolation range and from edge effects. By making predictions with purely lateral prediction filters, the distance the data is extrapolated in the spatial directions is extended. Also, although not well understood, the use of multiple directional prediction filters appears to improve the extrapolation quality, especially near the edges of the volume where very poor predictions are made. These three-dimensional directional filters are lateral filters with the output on one corner of the three-dimensional filter. While these results are preliminary, the techniques presented here look promising.