We explore the range of parameters for dark-matter sterile neutrinos in an extension of the Minimal Standard Model by three singlet fermions with masses below the electroweak scale (the νMSM). This simple model can explain a wide range of phenomena, including neutrino oscillations, baryogenesis, the pulsar velocities, and the early reionization. The presence of two heavier sterile neutrinos and the possibility of entropy production in their decays broadens the allowed range of parameters for the dark-matter sterile neutrinos (or other types of dark matter, for example, the gravitino). In addition, the primordial production of dark matter sterile neutrinos allows to escape most of the constraints. © 2006 Elsevier B.V. All rights reserved.