Detailed analysis of the distribution of craters on Venus using Mth nearest neighbor analysis, coupled with models based upon surface morphology constraints, indicates that the hypothesis of complete spatial randomness (CSR) cannot be rejected, but is not a unique model of the observed crater distribution. Based on morphologic mapping, the extensive volcanic plains can be divided into four units that have a spread in age of the order of 0.5T (the mean surface age of the planet). This four-unit plains model, along with its derivatives, produce test statistics that indicate such models also cannot be rejected. Further, the probability of obtaining a result at least as extreme as the observed test statistic given that the null hypothesis (model corresponds to Venus) is true is lowest for the CSR model. There is no particular reason to pick a CSR model (along with its implications for catastrophic resurfacing) as a constraint on the evolution of Venus, and there are geological reasons to choose the multiage models. We find that we cannot distinguish statistically among models that have two, three, or four distinct production ages within the plains. However, the hypothesis that the variation in crater density within all of the plains is due to a single random process can be rejected for two reasons. First, the binomial probability that such a process could exist within each of the plains units is ≤0.05 except the smallest and youngest unit, PLI. Second, using a chi-squared statistic to test the hypothesis that four plains units have the same age gives a p value of 10-4, indicating confident rejection of the hypothesis. Thus CSR cannot be used as a constraint on models of resurfacing or planetary evolution of Venus because of the non-uniqueness in matching such a model to the observed crater distribution and the strong indication of distinct ages within the plains with a significant spread in age. Geological and geophysical constraints provide our best clues for understanding Venus. ¿ 1998 American Geophysical Union