Executive tasks typically contain a prepotent lure. In addition, they require individuals either to (a) follow arbitrary procedures or (b) update their model of the physical world. Recent research suggests that children with autism may be challenged only by executive tasks of the former kind (containing arbitrary rules). We asked whether this continues to be true when there is no prepotent lure, comparing performance on (a) a task with arbitrariness but without prepotency with (b) a task with both features and (c) a task with neither. The participants with autism performed at a lower level than comparison groups on the first and second task but not on the third task. This outcome is consistent with the view that autism is associated with difficulties in following arbitrary procedures per se. We try to locate difficulties with acting on the basis arbitrary rules in relation to more mainstream ideas about autistic executive dysfunction.