Spindles are arrays of microtubules that segregate chromosomes during cell division. It has been difficult to validate models of spindle assembly due to a lack of information on the organization of microtubules in these structures. Here we present a method, based on femtosecond laser ablation, capable of measuring the detailed architecture of spindles. We used this method to study the metaphase spindle in Xenopus laevis egg extracts and find that microtubules are shortest near poles and become progressively longer towards the center of the spindle. These data, in combination with mathematical modeling, imaging, and biochemical perturbations, are sufficient to reject previously proposed mechanisms of spindle assembly. Our results support a model of spindle assembly in which microtubule polymerization dynamics are not spatially regulated, and the proper organization of microtubules in the spindle is determined by non-uniform microtubule nucleation and the local sorting of microtubules by transport.