Previous fits of sterile neutrino dark matter (DM) models to cosmological data ruled out masses smaller than approximately 8 keV, assuming a production mechanism that is not the best motivated from a particle physics point of view. Here we focus on a realistic extension of the standard model with three sterile neutrinos, consistent with neutrino oscillation data and baryogenesis, with the lightest sterile neutrino being the DM particle. We show that for each mass >or= 2 keV there exists at least one model accounting for 100% of DM and consistent with Lyman-alpha and other cosmological, astrophysical, and particle physics data.