A new generation of membranes for water purification based on weakly oxidized and nanoporous few-layer graphene is here introduced. These membranes dramatically decrease the high energy requirements of water purification by reverse osmosis. They combine the advantages of porous and non-oxidized single-layer graphene, offering energy-efficient water filtration at relatively low differential pressures, and highly oxidized graphene oxide, exhibiting high performance in terms of impurity adsorption. In the reported fabrication process, leaks between juxtaposed few-layer graphene flakes are sealed by thermally annealed colloidal silica, in a treatment that precedes the opening of (sub)nanometre-size pores in graphene. This process, explored for the first time in this work, results in nanoporous graphene flakes that are water-tight at the edges without occluding the (sub)nanopores. With this method, removal of impurities from water occurs through a combination of size-based pore rejection and pore-edge adsorption. Thinness of graphene flakes allows these membranes to achieve water purification from metal ions in concentrations of few parts-per-million at differential pressures as low as 30 kPa, outperforming existing graphene or graphene oxide purification systems with comparable flow rates.