Previous works in integro-difference models have generally considered Allee effects and overcompensation separately, and have focused on constant spreading speeds. In this talk, I will analytically demonstrate that for a piecewise constant growth function exhibiting both an Allee effect and overcompensation, there exist equilibrium solutions vanishing at infinity across solid regions of parameter space. I will numerically demonstrate that perturbations of the equilibrium solutions lead to solutions with various spatial patterns persisting essentially in compact domains.