The Australia Telescope National Facility Mopra millimetre telescope has been used to search for 95.1-GHz class I methanol masers towards 62 6.6-GHz class II methanol masers. A total of 26 95.1-GHz masers were detected, 18 of these being new discoveries. Combining the results of this search with observations reported in the literature, a near complete sample of 66 6.6-GHz class II methanol masers has been searched in the 95.1-GHz transition, with detections towards 38 per cent (25 detections; not all of the sources studied in this paper qualify for the complete sample, and some of the sources in the sample were not observed in the present observations).