The likelihood-ratio method for affected-sib-pair analysis, introduced by Risch, is a powerful method for detecting linkage when the marker is not perfectly polymorphic, as is often the case. The power of this method can be improved by restricting maximization to the set of possible haplotype-sharing probabilities--denoted the "possible triangle" method. The asymptotic distributions of the resulting distributions are derived, enabling test criteria to be found for any required test size (i.e., the probability of falsely detecting linkage when none exists) and enabling p values to be assigned to results. The criteria were found to be approximately constant when the PIC of the marker varies, making them applicable to any marker. The asymptotic power approximations were used to investigate the relative performance of pairs with typed parents, relative to those without, by comparing the sample sizes necessary for a given power. Under certain circumstances, typing the parents proved to be inefficient, even when PIC was low.