The cleaner wrasse Labroides dimidiatus occupies fixed ‘cleaning stations’ on coral reefs, which ‘client’ reef fish visit repeatedly to have parasites removed. Conflict arises because cleaners prefer to cheat by feeding on client mucus instead of parasites. Clients can prevent L. dimidiatus from always cheating using control mechanisms such as chasing and partner switching, which depend on repeated interactions. These control mechanisms would be undermined in the absence of frequent repeated interactions, if cleaners roved over large areas. Roving behaviour has been anecdotally described for the closely related cleaner wrasse Labroides bicolor. Here we report field data comparing these two species in Moorea, French Polynesia. Our results confirmed that L. bicolor home ranges are much larger than L. dimidiatus home ranges, and showed that cleaning interactions occurred all over the L. bicolor home range: home range of cleaning interactions increased with total home range size. Moreover, we found that cleaner initiation of interactions increased with home range size in L. bicolor, which would give L. bicolor with large home ranges additional leverage to increase cheating. In line with these results, we found that client jolt rate (used as a measure of cheating) was higher among clients of cleaners with large home ranges. Our results emphasise the importance of game structure and control over initiating interactions as parameters in determining the nature of interactions in mutualisms.