Our best estimates suggest that ~95% of dextrals and ~70% of adextrals have left hemisphere language dominance. Currently the only way to determine language lateralisation is to use invasive hemispheric anaesthetising procedures, or expensive functional neuroimaging methods. This lack of identification has led to adextrals being studied as an ‘atypical’ group in terms of functional lateralisation, despite the vast majority of them sharing the same brain organisation as dextral subjects. Therefore research into brain asymmetries or atypical dominance could progress much more quickly if a more successful predictor (or combination of predictors) of cerebral lateralisation than handedness were available. This body of work investigates the potential usefulness of behavioural, kinematic, and electrophysiological measures to predict cerebral asymmetries. These data are discussed in the first three experimental chapters, and the fourth chapter contains a neuroimaging project. In this final study language, face, and body processing asymmetries are identified in dextral and adextral participants who had taken part in the initial lab-based tests. The results from this thesis suggest that a consonant-vowel dichotic listening task, as well as strength of left-sidedness, may increase successful identification of ‘atypical’ language dominance beyond the 15% success of left-handed writing. Additionally, ear advantage on a further listening paradigm, the Octave illusion, differentiates between dextral and adextral subjects in a way that appears related to language lateralisation. Kinematic measures may be related to brain organisation, but the relationship is less clear than in the more successful behavioural lab tests. Finally, asymmetries in electrophysiological components are a poor predictor of functional lateralisation. This thesis advocates against the exclusive use of measures of central tendency, promoting alternative proportional and individual level analyses. This assessment has implications for laterality researchers using any methodology from behavioural neuropsychology to functional neuroimaging.