Permselective asymmetric membranes suitable e.g. for hemodialysis, hemodiafiltration and hemofiltration of blood, and having improved performance, including improved sieving characteristics, providing enhanced removal of middle molecular weight substances, e.g. inflammatory mediators having a molecular weight between 20 and 40 kDa. The improved sieving characteristics are due to a narrow pore size distribution of the membranes created in the production process. Processes for the preparation of these membranes, devices comprising these membranes, and the use of these membranes in hemodialysis, hemodiafiltration and hemofiltration of blood, as well as in bioprocessing, plasma fractionation and the preparation of protein solutions.