Mitotic spindles of Schizosaccharomyces pombe have been studied by EM, using serial cross sections to reconstruct 12 spindles from cells that were ultrarapidly frozen and fixed by freeze substitution. The resulting distributions of microtubules (MTs) have been analyzed by computer. Short spindles contain two kinds of MTs: continuous ones that run from pole to pole and MTs that originate at one pole and end in the body of the spindle. Among the latter there are three pairs of MT bundles that end on fibrous, darkly staining structures that we interpret as kinetochores. The number of MTs ending at each putative kinetochore ranges from two to four; all kinetochore-associated MTs disappear as the spindle elongates from 3-6 microns. At this and greater spindle lengths, there are no continuous MTs, only polar MTs that interdigitate at the spindle midzone, but the spindle continues to elongate. An analysis of the density of neighboring MTs at the midzone of long spindles shows that their most common spacing is approximately 40 nm, center to center, and that there is a preferred angular separation of 90 degrees. Only hints of such square-packing are found at the midzone of short spindles, and near the poles there is no apparent order at any mitotic stage. Our data suggest that the kinetochore MTs (KMTs) do not interact directly with nonkinetochore MTs, but that interdigitating MTs from the two spindle poles do interact to form a mechanically stable bundle that connects the poles. As the spindle elongates, the number of MTs decreases while the mean length of the MTs that remain increases. We conclude that the chromosomes of S. pombe become attached to the spindle by kinetochore MTs, that these MTs disappear as the chromosomes segregate, that increased separation of daughter nuclei is accompanied by a sliding apart of anti-parallel MTs, and that the mitotic processes of S. pombe are much like those in other eukaryotic cells.