A common approach for detecting genetic linkage using siblings is to collect affected sib pairs (ASPs) and to identify markers where allele sharing exceeds expectation. Alternatively, markers can be analyzed in discordant sib pairs (DSPs) for allele sharing below expectation. Relative to the ASP approach, according to Risch, the power of the DSP approach increases with sibling recurrence risk, the two approaches being equally effective at 50% recurrence risk. However, with many diseases associated with more moderate sibling recurrence risk, less emphasis has been placed on the use of DSPs and the development of the underlying theory. In this paper, we expand the work of Risch to provide a more general foundation for DSP studies, since power can be quite high under the appropriate conditions. For example, in some highly affected populations, such as the diabetes-prone Pima Indians, sibling recurrence risk can be very large and, thus, DSPs ideal. Similarly, as we show through simulation, DSPs are preferable for diabetic nephropathy due to a 70% recurrence rate among siblings with insulin-dependent diabetes mellitus. Following the diabetic nephropathy example, we consider more systematically the situations in which DSPs can provide an efficient alternative to ASPs.