A new density fitting approach to the Coulomb problem in Kohn-Sham and Hartree-Fock theory is introduced. Almost all of the 2- and 3-index repulsion integrals become simple overlap-like integrals, without approximation. The method is tested on numerous benchmark problems, which reveal that accuracy equal to or better than standard density fitting can be achieved with the evaluation of around a tenth of the number of Coulomb integrals. The scaling properties of the method are illustrated for polyalanine helices up to Ala(16).