We investigate strategies for detecting linkage of recessive and partially recessive traits, using sibling pairs and inbred individuals. We assume that a genomewide search is being conducted and that locus heterogeneity of the trait is likely. For sibling pairs, we evaluate the efficiency of different statistics under the assumption that one does not know the true degree of recessiveness of the trait. We recommend a sibling-pair statistic that is a linear compromise between two previously suggested statistics. We also compare the power of sibling pairs to that of more distant relatives, such as cousins. For inbred individuals, we evaluate the power of offspring of different types of matings and compare them to sibling pairs. Over a broad range of trait etiologies, sibling pairs are more powerful than inbred individuals, but for traits caused by very rare alleles, particularly in the case of heterogeneity, inbred individuals can be much more powerful. The models we develop can also be used to examine specific situations other than those we look at. We present this analysis in the idealized context of a dense set of highly polymorphic markers. In general, incorporation of real-world complexities makes inbred individuals, particularly offspring of distant relatives, look slightly less useful than our results imply.