Estimation of genealogical relationships from genetic data provides an approach to answering many questions of population biology. In this estimation problem, previous work has shown that bilateral relatives such as full sibs may be more likely parents than the true parent individuals. This paper investigates the source of this paradox, and the circumstances under which it may arise. Alternative approaches to inferring parentage are proposed; these involve analysis of the distributions of log-likelihood statistics and of the bivariate distribution of sib and parent log-likelihoods. A Bayesian approach may also be superposed on the likelihood analysis, enabling any prior knowledge of the population to be incorporated.