The right shift (RS) theory of handedness and cerebral dominance (Annett, 1972, 1985) suggested that individual differences for patterns of cerebral dominance may be associated with different types of risk to cognitive functions. The higher prevalence of dextrality than sinistrality in humans depends on a single gene (RS+) which facilitates left hemisphere specialisation for speech but at the expense of some right hemisphere function (Annett, 1992b; Kilshaw and Annett, 1983). RS-- genotypes have random asymmetries for hand and brain while RS++ genotypes have strong right shift. Three samples of undergraduates were given tests of phonological processing and of real word homophone discrimination. As predicted, phonology was poor in comparison with homophone discrimination toward the left of the laterality continuum while the reverse was true to the right of the continuum. When groups with specific difficulty for each type of test in comparison with the other were distinguished, those with poor phonology were less dextral and those with poor homophone discrimination were more dextral for hand preference than the rest of the sample. Siblings differed for handedness also, consistent with the argument for a genetic influence.