Extended practice on a particular cognitive task can boost the performance of other tasks, even though they themselves have not been practiced. This transfer of benefits appears to be specific, occurring most when tasks are very similar to those being trained. But what type of similarity is most important for predicting transfer? This question is addressed with a tightly controlled randomised design, with a relatively large sample (N=175) and an adaptive control group. We created a hierarchical set of nested assessment tasks. Participants then trained on two of the tasks: one was relatively ‘low’ in the hierarchy requiring just simultaneous judgments of shapes’ spikiness, whereas the other was relatively ‘high’ requiring delayed judgments of shapes’ spikiness or number of spikes in a switching paradigm. Using the full complement of nested tasks before and after training we could then test whether and how these ‘low’ and ‘high’ training effects cascade through the hierarchy. For both training groups, relative to the control, whether or not an assessment task shared a single specific feature was the best predictor of transfer patterns. For the lower-level training group, the overall proportion of feature overlap also significantly predicted transfer, but the same was not true for the higher-level training group. Finally, pre-training between-task correlations were not predictive of the pattern of transfer for either group. Together these findings provide an experimental exploration of the specificity of transfer, and establish the nature of task overlap that is crucial for the transfer of performance improvements.