Model-free LOD-score methods are often employed to detect linkage between marker loci and common diseases, with samples of affected sib pairs. Although extensions of the basic one-disease-locus model have been proposed that allow separate inclusion of other types of affected relative pairs, discordant relative pairs, covariates, or additional disease loci, a unified framework that can handle all of these features has been lacking. In this report, I propose a conditional-logistic parameterization that generalizes easily to include all of these features. Two data examples, one using simulated data and one using type 1 diabetes, illustrate applications of the models.