A community assembly rule, applied to rodent communities of deserts of the American Southwest, suggests that local communities are competitively structured. Species composition appears more evenly distributed among functional groups than would have been expected had species entered local communities independently of other species that were already there. This suggestion is based on a greater number than expected of 'favored states' (local communities in which no two functional groups differ in the number of species by more than one). We randomized communities by two different methods and found that the observed number of favored states, though greater than that expected, is not in an extreme tail of the simulated distribution, so that one would not have rejected a hypothesis that species join local communities independently. The suggested result, contradicted by our findings, is probably an artifact of the fact that the previous assembly rule treated all species as equally likely to be found on all sites. Further, we found that the excess of the observed number of favored states over that expected by our two methods can probably be explained by the fact that the few widespread species are not treated realistically. Our analysis overcomes a previous methodological problem (the Narcissus effect) in which the null model is not truly null with respect to competition. Additionally, our techniques provide a means of exploring the spatial structure in the nonrandom distribution of species.