The degree to which executive function (EF) abilities (including working memory (WM), inhibitory control (IC), and cognitive flexibility (CF)) can be enhanced through training is an important question, however research in this area is inconsistent. Previous cognitive training studies largely agree that training leads to improvements in the trained task, but the generalizability of this improvement to other related tasks remains controversial. In this paper, we present a pre-registered experiment that used an adaptive training procedure to examine whether EFs can be enhanced through cognitive training, and directly compared the efficacy and generalisability across sub-components of EF using training programs that target WM, IC or CF vs. an active control group. Participants (n=160) first completed a battery of tasks that assessed EFs, then were randomly assigned to one of four training groups, and completed an adaptive procedure over 21 days (10 training sessions) that targeted a specific sub-component of EF (or was comparatively engaging and challenging, but did not train a specific EF). At post-test, participants returned to the lab to repeat the battery of EF tasks. Results revealed robust direct training effects (i.e. on trained task), but limited evidence to support near (i.e. same EF, different task) and far (i.e. different EF and task) transfer effects. Where indirect training benefits emerged, the effects were more readily attributable to the overlapping training/assessment task routines, rather than more general enhancements to the underlying cognitive processes or neural circuits.