Graphene oxide (GO) membranes continue to attract intense interest due to their unique molecular sieving properties combined with fast permeation1-9. However, their use is limited to aqueous solutions because GO membranes appear impermeable to organic solvents(1), a phenomenon not yet fully understood. Here, we report effcient and fast filtration of organic solutions through GO laminates containing smooth two-dimensional (2D) capillaries made from large (10-20 mu m) flakes. Without modification of sieving characteristics, these membranes can be made exceptionally thin, down to similar to 10 nm, which translates into fast water and organic solvent permeation. We attribute organic solvent permeation and sieving properties to randomly distributed pinholes interconnected by short graphene channels with a width of 1 nm. With increasing membrane thickness, organic solvent permeation rates decay exponentially but water continues to permeate quickly, in agreement with previous reports1-4. The potential of ultrathin GO laminates for organic solvent nanofiltration is demonstrated by showing >99.9% rejection of small molecular weight organic dyes dissolved in methanol. Our work significantly expands possibilities for the use of GO membranes in purification and filtration technologies.