We present a computer simulation of group selection that is inspired by proto-cell division. Two types of replicating molecules, cooperators and defectors, reside inside membrane bound compartments. Cooperators pay a cost for other replicators in the cell to receive a benefit. Defectors pay no cost and distribute no benefits. The total population size fluctuates as a consequence of births and deaths of individual replicators. Replication requires activated substrates that are generated at a constant rate. Our model includes mutation between cooperators and defectors and selection on two levels: within proto-cells and between proto-cells. We find surprising similarities and differences between models with and without cell death. In both cases, a necessary requirement for group selection to favor some level of cooperation is the continuous formation of a minimum fraction of pure cooperator groups. Subsequently these groups become undermined by defectors, because of mutation and selection within cells. Cell division mechanisms which generate pure cooperator groups more efficiently are stronger promoters of cooperation. For example, division of a proto-cell into many daughter cells is more powerful in enhancing cooperation than division into two daughter cells. Our model differs from previous studies of group selection in that we explore a variety of different features and relax several restrictive assumptions that would be needed for analytic calculations.