We consider three tests for genetic association in data from nuclear families (the Family-Based Association Test (FBAT) test proposed by Rabinowitz and Laird ( Hum. Hered. 50:211–223), a second test proposed by Rabinowitz ( J. Am. Stat. Assoc. 97:742–758), and the Family Genotype Analysis Program (FGAP) nonfounder or partial score test proposed by Clayton ( Am. J. Hum. Genet. 65:1170–1177) and Whittemore and Tu ( Am. J. Hum. Genet. 66:1329–1340)). We show that each test statistic arises from the efficient score of the family data as the solution to a set of constraints on its null expectation. Moreover, the FBAT and Rabinowitz tests (but not the FGAP test) are locally the most powerful among all tests satisfying their constraints. We used simulations to examine how the three tests perform in situations when their assumptions are violated and the number of families is not huge. We found that the FBAT test tended to have less power than the other two tests, particularly when applied to families in whom all offspring were affected. The Rabinowitz and FGAP tests performed similarly, although the latter tended to extract more information from families containing one typed parent. While none of the tests showed good power to detect rare, recessively acting genes, the Rabinowitz test with a sample variance estimate performed particularly poorly in this case. However, the Rabinowitz test with a model-based variance had power comparable to that of the FGAP test, and more accurate type I error rates. We conclude that for the situations we considered, the Rabinowitz test with model-based variance has good power without forfeiting robustness against misspecification of parental genotype probabilities. However, its utility is limited by the lack of a simple algorithm to apply it to families with varying structures and phenotypes. Genet Epidemiol 25:80–91, 2003. © 2003 Wiley-Liss, Inc.