The classical framework of context-tree models used in sequential decision problems such as compression and prediction is generalized to a setting in which the observations are multi-tracked, multi-sided, or multi-directional, and for which it may be beneficial to consider contexts comprised of possibly differing numbers of symbols from each track or direction. Tree representations of context sets and pruning algorithms for those trees are extended from the uni-directional setting to two directions. We further show that such tree representations do not extend, in general, to m directions, m >; 2, and that, as a result, determining the best m-directional context set for m >; 2 may be substantially more complex than in the case of m ≤ 2. An application of the proposed pruning algorithm to denoising, where m=2 , is presented.