Historically, most theoretical accounts of hemispheric specialisation have proposed a single underlying factor that leads to left hemisphere language and right hemisphere visuospatial processing in the majority of people. More recently empirical evidence has started to challenge this view, suggesting lateralisation of language and visuospatial attention are independent. However, so far studies did not control for a possible confound, task difficulty. For this study, 20 healthy right-handed volunteers underwent functional laterality assessment using functional transcranial Doppler ultrasound (fTCD). We assessed laterality using both a word generation task and a novel variation of the visuospatial landmark task that can be adjusted along two dimensions of difficulty (temporal and spatial). The visuospatial laterality measures were highly intercorrelated and unaffected by task difficulty. Furthermore, there was no correlation between visuospatial and verbal lateralisation within individuals – neither qualitatively (in direction of lateralisation), nor quantitatively (in laterality index size). These results substantiate a growing body of evidence suggesting multiple independent biases leading to the hemispheric lateralisation of different cognitive domains, thus further questioning previously accepted models of laterality development and evolution.