We perform a detailed analysis of baryon asymmetry generation in the NuMSM (an extension of the Standard Model by three singlet Majorana fermions with masses below the Fermi scale). Fixing a number of parameters of the NuMSM by the neutrino oscillation data, we determine the remaining domain of the parameter space from the requirement of successful baryogenesis. We derive, in particular, the constraints on the mass splitting of a pair of singlet fermions, and on the strength of their coupling to ordinary leptons, essential for searches of these particles in rare decays of mesons and in beam-dump experiments with intensive proton beams.