Abstract Improvements in behaviour are known to be accompanied by both structural and functional changes in the brain. However whether those changes lead to more general improvements, beyond the behaviour being trained, remains a contentious issue. We investigated whether training on one of two cognitive tasks would lead to either near transfer (that is, improvements on a quantifiably similar task) or far transfer (that is, improvements on a quantifiably different task), and furthermore, if such changes did occur, what the underlying neural mechanisms might be. Participants trained on either a verbal inhibitory control task or a visuospatial working memory task for four weeks, over the course of which they received five diffusion tensor imaging scans. Two additional tasks, a test of verbal reasoning and a test of spatial span, served as measures of near transfer for the inhibitory control task and spatial working memory task, respectively. These two tasks also served as measures of far transfer for the alternate training task. Behaviourally, participants improved on the task that they trained on, but did not improve on cognitively similar tests (near transfer), nor cognitively dissimilar tests (far transfer). Extensive changes to white matter microstructure were observed, with verbal inhibitory control training leading to changes in a left-lateralized network of fronto-temporal and occipito-frontal tracts, and visuospatial working memory training leading to changes in right-lateralized fronto-parietal tracts. Very little overlap was observed in changes between the two training groups. On the basis of these results, we suggest that near and far transfer were not observed because the changes in white matter tracts associated with training on each task are almost entirely non-overlapping with, and therefore afford no advantages for, the untrained tasks.