Straightforward isocontouring techniques examine each cell of a mesh to test for intersection with the isocontour of interest. Accelerated isocontouring can be achieved by preprocessing of the data to establish a "seed set" of cells which contains at least one cell from each connected component of each isocontour. From this typically small set of cells, we apply contour propagation to track a contour through cell adjacencies. To provide an advantage in worst-case computational complexity, the seed set is further preprocessed into an optimal O(log n) search structure, such as the interval tree or segment tree. Total complexity is O(log n + k), where n is the size of the seed set, and k is the number of cells intersected by the surface. In practice, speedups of 2-40 times are achieved.