Mindfulness meditation programs, which train individuals to monitor their present-moment experience in an open or accepting way, have been shown to reduce mind wandering on standardized tasks in several studies. Here we test 2 competing accounts for how mindfulness training reduces mind wandering, evaluating whether the attention-monitoring component of mindfulness training alone reduces mind wandering or whether the acceptance training component is necessary for reducing mind wandering. Healthy young adults (N = 147) were randomized to either a 3-day brief mindfulness training condition incorporating instruction in both attention monitoring and acceptance, a mindfulness training condition incorporating attention monitoring instruction only, a relaxation training condition, or an active reading-control condition. Participants completed measures of dispositional mindfulness and treatment expectancies before the training session on Day 1 and then completed a 6-min Sustained Attention to Response Task (SART) measuring mind wandering after the training session on Day 3. Acceptance training was important for reducing mind wandering, such that the attention-monitoring plus acceptance mindfulness training condition had the lowest mind wandering relative to the other conditions, including significantly lower mind wandering than the attention-monitoring only mindfulness training condition. In one of the first experimental mindfulness training dismantling studies to-date, we show that training in acceptance is a critical driver of mindfulness-training reductions in mind wandering. This effect suggests that acceptance skills may facilitate emotion regulation on boring and frustrating sustained attention tasks that foster mind wandering, such as the SART.