Melody lateralisation has been examined extensively, using well known behavioural techniques−dichotic/monaural listening and dual tasks. The literature using these techniques has produced paradoxical results for the lateralisation of melody processing particularly with non-musicians. Research using the dichotic/monaural listening paradigm suggests right hemisphere processing for non-musicians while the dual task paradigm has suggested a left hemisphere dominance. The current study utilises both monaural listening and dual task techniques within trials. The results replicated the paradox in the literature. The dichotic/monaural listening melody measure (d ') suggest right hemisphere processing of melodies for both musicians and non-musicians. In contrast, the dual task measure suggests left hemisphere processing for the non-musicians and bilateral processing for the musicians. Both measures were collected from the same stimulus presentations and are therefore paradoxical particularly for the non-musicians. Irrespective of which task participants are primarily attending, both laterality measures should produce internally consistent patterns if they are measuring the same aspects of melody processing. Although the paradox for the musicians may be resolved by postulating an attentional bias towards the tapping task, no such explanation is possible for the non-musicians. In light of the paradoxical findings produced by these two measures, their utility for providing unambiguous information about lateralisation of mental processing is questionable.