Many neuroscientific techniques have revealed that more left- than right-handers will have unusual cerebral asymmetries for language. After the original emphasis on frequency in the aphasia and epilepsy literatures, most neuropsychology and neuroimaging efforts rely on measures of central tendency to compare these two handedness groups on any given measure of asymmetry. The inevitable reduction in mean asymmetry in the left-handed group is often postulated as being due to reversed asymmetry in a small subset of them, but it could also be due to a reduced asymmetry in many of the left-handers. These two possibilities have hugely different theoretical interpretations. Using fMRI localiser paradigms, we matched left- and right-handers for hemispheric dominance across four functions (verbal fluency, face perception, body perception, scene perception). We then compared the degree of dominance between the two handedness groups for each of these four measures, conducting t-tests on the mean laterality indices. The results demonstrate that left-handers with typical cerebral asymmetries are less lateralized for language, faces and bodies than their right-handed counterparts. These results are difficult to reconcile with current theories of language asymmetry or of handedness.