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A prior study showed that rhythmic, but not arrhythmic, 12 Hz stimulation of the median nerve (MNS) entrained sensorimotor cortex EEG signal, and found that 10 Hz MNS improved tics in Tourette syndrome (TS). However, no control condition was tested and stimulation blocks lasted only 1 minute. We set out to replicate the TS results and to test whether tic improvement occurs by the proposed cortical entrainment mechanism. Thirty-two people with TS, age 15-64, completed two study visits with repeated MNS on and off blocks in random order, one visit for rhythmic and one for arrhythmic MNS. Subjects and staff were blind to order; a video rater was additionally blind to stimulation and to order of visits and blocks. Rhythmic MNS at 10 Hz improved tics. Both rhythmic and arrhythmic 12 Hz MNS improved tic frequency, intensity and urges without significant difference. Participant masking was effective and there was no carryover effect. Several participants described dramatic benefit. Discomfort was minimal. MNS benefit did not persist after the end of stimulation. These results replicate the tic benefit from MNS, but show that the EEG entrainment hypothesis cannot explain that benefit. Another electrophysiological mechanism may explain benefit; alternatively, these data do not exclude a placebo effect., Registration: ClinicalTrials.gov , NCT04731714 .