Diffusion MRI (dMRI) tractography is a uniquely powerful tool capable of demonstrating structural brain network abnormalities across a range of psychiatric disorders; however, it is not currently clinically useful. This is because limitations on sensitivity effectively restrict its application to scientific studies of cohorts, rather than individual patients. Recent improvements in dMRI hardware, acquisition, processing and analysis techniques may, however, overcome these measurement limitations. We therefore acquired the highest-ever angular resolution in vivo tractographic data set, and used these data to ask the question: 'is cutting-edge, optimised dMRI now sensitive enough to measure brain network abnormalities at a level that may enable personalised psychiatry?' The fibre tracking performance of this 'gold standard' data set of 1150 unique directions (11 shells) was compared to a conventional 64-direction protocol (single shell) and a clinically practical, highly optimised and accelerated 9-min protocol of 140 directions (3 shells). Three major tracts of relevance to psychiatry were evaluated: the cingulate bundle, the uncinate fasciculus and the corticospinal tract. We found up to a 34-fold improvement in tracking accuracy using the 1150-direction data set compared to the 64-direction data set, while 140-direction data offered a maximum 17-fold improvement. We also observed between 20 and 50% improvements in tracking efficiency for the 140-direction data set, a finding we then replicated in a normal cohort (n = 53). We found evidence that lower angular resolution data may introduce systematic anatomical biases. These data highlight the imminent potential of dMRI as a clinically meaningful technique at a personalised level, and should inform current practice in clinical studies.