We have made polyvinylalcohol membranes containing mordenite which have twenty times better selectivity for protons over methanol than perfluorinated sulfonic acid polymers. Membranes like these should improve the efficiencies of fuel cells fed directly with methanol. Our results show that further improvements are possible with composite membranes, but that these improvements will require polymers less conductive than those currently used. This is the opposite of conventional wisdom.