Theories make varying predictions regarding the functional form of the relationship between neighborhood poverty and crime rates, ranging from a diminishing positive effect, to a linear positive effect, to an exponentially increasing or even threshold effect. Nonetheless, surprisingly little empirical evidence exists testing this functional form. This study estimates the functional form of the relationship between poverty and various types of serious crime in a sample of census tracts for 25 cities, and it finds that a diminishing positive effect most appropriately characterizes this relationship whether estimating the models nonparametrically or parametrically. Only for the crime of murder does some evidence exist of an accelerating effect, although this occurs in the range of 20 to 40 percent in poverty, with a leveling effect on crime beyond this point of very high poverty. Thus, no evidence is found here in support of the postulate of scholars extending William Julius Wilson's (1987) insight that neighborhoods with very high levels of poverty will experience an exponentially higher rate of crime compared with other neighborhoods. (Published Abstract)