AIMS: A large number of studies have found links between alcohol outlet densities and assault rates in local areas. This study tests a variety of specifications of this link, focusing in particular on the possibility of a non-linear relationship. DESIGN: Cross-sectional data on police-recorded assaults during high alcohol hours, liquor outlets and socio-demographic characteristics were obtained for 223 postcodes in Melbourne, Australia. These data were used to construct a series of models testing the nature of the relationship between alcohol outlet density and assault, while controlling for socio-demographic factors and spatial auto-correlation. Four types of relationship were examined: a normal linear relationship between outlet density and assault, a non-linear relationship with potential threshold or saturation densities, a relationship mediated by the socio-economic status of the neighbourhood and a relationship which takes into account the effect of outlets in surrounding neighbourhoods. FINDINGS: The model positing non-linear relationships between outlet density and assaults was found to fit the data most effectively. An increasing accelerating effect for the density of hotel (pub) licences was found, suggesting a plausible upper limit for these licences in Melbourne postcodes. CONCLUSIONS: The study finds positive relationships between outlet density and assault rates and provides evidence that this relationship is non-linear and thus has critical values at which licensing policy-makers can impose density limits.