Genetic studies of complex diseases must confront two statistically difficult issues simultaneously. First, in many settings, to minimize the number of individuals to be genotyped, families enriched for disease must be oversampled. Also, statistical models in family studies should allow for residual association. This association will represent unmeasured genetic and environmental factors influencing disease risk. Dealing with these features simultaneously is both compelling and challenging. Burton et al. [2000] (Am. J. Hum. Gen. 69: 1505–14) recently discussed this issue and suggested that ascertainment corrections may lead to problematic parameter estimation. We revisit the issues and examples of Burton et al. [2000] (Am. J. Hum. Genet. 69: 1505–14) and present a more optimistic assessment. Estimation in this context is conceptually straightforward, but may be more problematic in practice. Specifically, we find that even slight misspecification of the random effects distribution in ascertainment‐adjusted likelihood can yield severely biased parameter estimates. This result should make scientists wary when interpreting results from ascertainment‐adjusted variance‐component models. Genet. Epidemiol. 23:201–208, 2002. © 2002 Wiley‐Liss, Inc.