Standard variance-components quantitative trait loci (QTL) linkage analysis can produce an elevated rate of type 1 errors when applied to selected samples and non-normal data. Here we describe an adjustment of the log-likelihood function based on conditioning on trait values. This leads to a likelihood ratio test that is valid in selected samples and non-normal data, and equal in power to alternative methods for analyzing selected samples that require knowledge of the ascertainment procedure or the trait values of non-selected individuals.