Twin concordance rates are usually reported without reference to the number of parents affected, apparently because the simple demonstration that monozygotic (MZ) twins are more concordant than are dizygotic (DZ) twins is the goal of most twin studies. Depending on the underlying mechanism, however, twin concordance rates can vary widely when conditioned on the number of parents affected. For the generalized single-locus model it is shown that conditional concordance rates in monozygotic twins, along with an estimate of the disorder's prevalence in the population, uniquely specify the underlying parameters of this important model. Knowledge of the exact parameter set is essential for competent genetic counseling.