Instead of creating the observed baryon asymmetry of the universe by the decay of right-handed (RH) neutrinos to left-handed leptons, we propose to generate it dominantly by the decay of the RH neutrinos to RH leptons. This mechanism turns out to be successful in large regions of parameter space. It may work, in particular, at a scale as low as ∼ TeV, with no need to invoke quasi-degenerate RH neutrino masses to resonantly enhance the asymmetry. Such a possibility can be probed experimentally by the observation at colliders of a singlet charged Higgs particle and of RH neutrinos. Other mechanisms which may lead to successful leptogenesis from the RH lepton sector interactions are also briefly presented. The incorporation of these scenarios in left-right symmetric and unified models is discussed.