In children with Tourette syndrome (TS), tics are often attributed to deficient self-control by health-care professionals, parents, and peers. In this behavioural study, we examined response inhibition in TS using a modified Simon task which probes the ability to solve the response conflict between a new non-spatial rule and a highly-overlearned spatial stimulus-response mapping rule. We applied a distributional analysis to the behavioural data, which grouped the trials according to the individual distribution of reaction times in four time bins. Distributional analyses enabled us to probe the children's ability to control fast, impulsive, responses, which corresponded to the trials in the fastest time bin. Additionally, we tested whether the ability to suppress inappropriate action tendencies can be improved further by the prospect of a reward. Forty-one clinically well-characterized medication-naïve children with TS, 20 children with attention-deficit/hyperactivity disorder (ADHD), and 43 typically developing children performed a Simon task during alternating epochs with and without a prospect of reward. We applied repeated measures ANCOVAs to estimate how the prospect of reward modulated reaction times and response accuracy, while taking into account the distribution of the reaction times across trials. We found between-group differences in accuracy when subjects responded relatively fast. The TS group responded more accurately than typically developing control children when resolving the response conflict introduced by the Simon task. The opposite pattern was found in children with ADHD. Prospect of reward improved accuracy rates in all groups. Although the Tourette group performed with superior accuracy in the fast trials, it was still possible for them to benefit from prospect of reward in fast trials. The findings corroborate the notion that children with TS have an enhanced capacity to inhibit fast inappropriate response tendencies. This ability can be improved further by offering a prospect of reward which might be useful during non-pharmacological therapeutic interventions.