Several non-verbal perceptual and attentional processes have been linked with specialization of the right cerebral hemisphere. Given that most people have a left hemispheric specialization for language, it is tempting to assume that functions of these two classes of dominance are related. Unfortunately, such models of complementarity are notoriously hard to test. Here we suggest a method which compares frequency of a particular perceptual asymmetry with known frequencies of left hemispheric language dominance in right-handed and non-right handed groups. We illustrate this idea using the greyscales and colourscales tasks, chimeric faces, emotional dichotic listening, and a consonant-vowel dichotic listening task. Results show a substantial "breadth" of leftward bias on the right hemispheric tasks and rightward bias on verbal dichotic listening. Right handers and non-right handers did not differ in terms of proportions of people who were left biased for greyscales/colourscales. Support for reduced typical biases in non-right handers was found for chimeric faces and for CV dichotic listening. Results are discussed in terms of complementary theories of cerebral asymmetries, and how this type of method could be used to create a taxonomy of lateralized functions, each categorized as related to speech and language dominance, or not.