The classic variance components for simple polygenic traits - additive, dominance, and environmental variance - have traditionally been estimated from sample covariances between first-degree relatives. If data is gathered on pedigrees, this statistical procedure wastes information. Recently Elston & Stewart suggested an alternative likelihood procedure that uses all the information in a set of pedigrees. A refinement of their method based on the scoring technique gives rapidly converging maximum likelihood estimates of the variance components and of the male and female means. Tests of statistical hypotheses about the various parameters can then be made by the likelihood ratio method. Furthermore, using classical regression analysis, the estimated parameter values allow prediction of unknown trait values from known trait values within a pedigree. These methods should apply to traits like total finger ridge count and to quantitative measurements associated with disease traits. Since the model postulates independent environmental effects and no assortative mating, its utility in human behaviour genetics seems limited.