We have generalized the Nanbu collision algorithm to accommodate arbitrary collision rates, enabling accurate kinetic modeling of short range particle interactions in non-Spitzer systems. With this extension, we explore the effect of different collision models on the simulation of how ultraintense lasers first begin to heat a target. The effect of collisions on plasma evolution is crucial for treating particle slowing, energy transport, and thermalization. The widely used Nanbu collision algorithm provides a fast and computationally efficient method to include the effects of collisions between charged particles in kinetic simulations without requiring that the particles already be in local thermal equilibrium. However, it is "hardwired" to use Spitzer collision rates appropriate for hot, relatively dilute plasmas. This restriction prevents the Nanbu collision algorithm from accurately describing the initial heating of a cold target, a key problem for the study of laser damage or the generation of the warm dense matter state. We describe our approach for modifying the Nanbu collision algorithm and demonstrate the improved accuracy for copper targets.