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Researchers of mind wandering frequently assume that (a) participants are motivated to do well on the tasks they are given, and (b) task-unrelated thoughts (TUTs) that occur during task performance reflect unintentional, unwanted thoughts that occur despite participants' best intentions to maintain task-focus. Given the relatively boring and tedious nature of most mind-wandering tasks, however, there is the possibility that some participants have little motivation to do well on such tasks, and that this lack of motivation might in turn result in increases specifically in "intentional" TUTs. In the present study, we explored these possibilities, finding that individuals reporting lower motivation to perform well on a sustained-attention task reported more intentional relative to unintentional TUTs compared with individuals reporting higher motivation. Interestingly, our results indicate that the extent to which participants engage in intentional versus unintentional TUTs does not differentially relate to performance: both types of off-task thought were found to be equally associated with performance decrements. Participants with low levels of task-motivation also engaged in more overall TUTs, however, and this increase in TUTs was associated with greater performance decrements. We discuss these findings in the context of the literature on mind wandering, highlighting the importance of assessing the intentionality of TUTs and motivation to perform well on tasks assessing mind wandering.