Spatial structure has been shown to promote altruistic behavior, however, it also increases the intensity of competition among relatives. Our purpose here is to develop a model in which this competition is minimized, more precisely a local increase in fecundity has a minimal competitive effect on the fitness of nearby individuals. We work with an island model in which sites are allowed to be empty, choosing our demographic rules so that in patches with higher fecundity, empty sites are filled at a higher rate. We also allow dispersal rates to evolve in response to the proportion of empty sites in the patch. Patches with different numbers of empty sites differ in frequency, in within-patch consanguinity, and in reproductive value. Using an inclusive fitness argument, we show that our model does promote altruism; indeed Hamilton's Rule is shown to hold. The only negative effect on an actor of a gift of fecundity to a patchmate turns out to be a slight decrease in reproductive value due to an increased probability of an empty site being occupied. We show that altruists are most favored in islands with an intermediate number of empty sites.