When analysing the mode of inheritance of a genetic trait, or mapping its location on the human genome, computationally intensive likelihood calculations are required. The standard method, called peeling, is reviewed here and an extension to the calculation of gradients is implemented. The gradients are used for numerical searches for maximum likelihood estimates, and also for producing contour plots of log-likelihood surfaces. This is illustrated with an analysis of the mode of inheritance, of the eye disease blue dot cataract, and of its proximity to a genetic marker on chromosome 16.