Although most mutations are deleterious, an interplay between somatic mutation and selection within germinal centers (GC) results in rapid generation of high affinity memory B cells. How high affinity B cells with large numbers of mutations are generated and preserved within GC containing at their peak only a few thousand cells has been puzzling. We have developed a model of somatic mutation and B cell expansion within a GC that resolves this puzzle. We show that the frequent recycling of Ag-selected centrocytes back into centroblasts can lead to efficient affinity maturation. Memory cells are generated in large numbers even when most of the selected centrocytes recycle back into centroblasts. Our model suggests that a germinal center reaction in which the output of cells is low up to the point of GC dissociation, followed by the release of centrocytes into the periphery, is advantageous for generating high affinity memory.