An approach commonly used to increase statistical power in linkage studies is the study of extremely discordant sibling pairs. This design is powerful under both additive and dominant-gene models and across a wide range of allele frequencies. A practical problem with the design is that extremely discordant pairs that are ostensibly full sibs may be half sibs. Although estimates vary, the population rates of such nonpaternity may be as high as 5%-10%. The proportion in discordant pairs may be much higher. The present article explores this potential inflation as a function of the resemblance of sib pairs and the criteria for discordance used for selection.