Apert syndrome is almost always caused by a spontaneous mutation of paternal origin in one of two nucleotides in the fibroblast growth factor receptor 2 gene (FGFR2). The incidence of this disease increases with the age of the father (paternal age effect), and this increase is greater than what would be expected based on the greater number of germ-line divisions in older men. We use a highly sensitive PCR assay to measure the frequencies of the two causal mutations in the sperm of over 300 normal donors with a wide range of ages. The mutation frequencies increase with the age of the sperm donors, and this increase is consistent with the increase in the incidence rate. In both the sperm data and the birth data, the increase is non-monotonic. Further, after normalizing for age, the two Apert syndrome mutation frequencies are correlated within individual sperm donors. We consider a mathematical model for germ-line mutation which reproduces many of the attributes of the data. This model, with other evidence, suggests that part of the increase in both the sperm data and the birth data is due to selection for mutated premeiotic cells. It is likely that a number of other genetic diseases have similar features.