A model of tandem charge-carrier photogeneration in disordered organic materials at low excess photon energies above the absorption edge is formulated. It suggests that relaxed singlet excitons dissociate into strongly bound metastable short off-chain geminate pairs. In parallel, triplet excitons can be generated from both primary singlets and short geminate pairs. Owing to a long intrinsic lifetime of triplets, most of them are quenched by geminate pairs and the latter can gain additional energy that facilitates transformation of short pairs into longer ones. This reduces the Coulomb binding energy such that field-assisted full dissociation into free carriers becomes feasible.