The hand preferences of Open University (OU) students and their relatives, including children, are described. As in earlier series, estimates of heritability are higher for mothers than fathers. There is no evidence of smaller heritability for paternal than maternal grandparents. The distribution of left-handedness in families is examined in the light of predictions of the right shift theory and on the assumption that the shift depends on a single gene. Good agreement is found between the observed and expected numbers of R x R, L x R and L x L families. Predictions are successful for both strict and generous criteria of sinistrality. Generation differences are found between OU students and their parents and between the students and their children. These are discussed from the viewpoint of a possible heterozygote advantage in intelligence. The higher proportion of sinistral children born to sinistral mothers than fathers can be partly accounted for by supposing that the right shift is more effective in females than males.