Previous maximum likelihood methods to analyze quantitative data on two inbred parental strains, their F1 and backcross generations are extended in three directions: (1) a method is suggested to transform the data to better satisfy the assumptions of normality and homoscedasticity; (2) the likelihoods are modified to allow for litter correlations and heteroscedasticity and (3) allowance is made for the incorporation of F2 data. The problem of making a choice among a set of simple genetic hypotheses is further discussed.