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Ten mitotic spindles from Dictyostelium discoideum have been studied by electron microscopy of serial sections. We have used computer graphics to track individual microtubules (MTs) in three dimensions and to compare seven spindles at different stages of anaphase and telophase. The central spindle of early anaphase is formed by the interdigitation of two sets of pole-associated MTs. The distribution of MT lengths at this stage is hetero-disperse. During anaphase total MT length decreases by a factor of about 2 as a result of two opposing changes in MT length: the longer MTs that interdigitate become even longer, while the short MTs, including those attached to kinetochores, become shorter still and decrease in number. The extent of MT interdigitation is less in longer spindles than in short ones. In metaphase and early anaphase, the MTs are not in an ordered arrangement as seen in spindle cross-sections, but as anaphase proceeds the MTs cluster into a square-packed, paracrystalline bundle in which most of the nearest neighbours come from opposite poles. This arrangement and the condensation-like increase in order suggest the existence of specific interactions between antiparallel MTs. A quantitative analysis of MT positions supports this interpretation, but direct evidence for convincing bridges between MTs is lacking. The pole-distal ends of the MTs that interdigitate show an irregular termination (C-shaped ends in transverse view), as is characteristic of MTs that are either adding or losing subunits. Since it is these interdigitating MTs that elongate, and since the shortening MTs show the customary blunt endings, we conclude that subunits add to the interdigitating MTs at their pole-distal ends. This inference, combined with other structural data, suggests that the interdigitating MTs of Dictyostelium are sliding over one another as they polymerize in anaphase. It also suggests a simple model for why the spindle becomes thinner as it elongates. We propose that MT interdigitation defines a region where MTs bind a factor that will associate only with antiparallel MTs. This factor biases the MT assembly equilibrium toward polymer. As the shorter MTs slide out of this region, they lose their polymerization advantage and depolymerize, releasing subunits to contribute to the further elongation of the already longer MTs. The properties of the Dictyostelium spindle are compared with those of both higher and lower eukaryotes.