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The standard model left-handed neutrinos and several right-handed neutrinos can obtain a tiny Dirac mass matrix through their mixings with relatively heavy Dirac fermions. In this Dirac seesaw scenario, the mixings involving the left-handed neutrinos can be allowed much larger than those involving the right-handed neutrinos. This undemocratic parameter choice is attractive to phenomenology. We show that the small mixings between the heavy Dirac fermions and the right-handed neutrinos can have a common origin with the observed baryon asymmetry in the universe. We also connect the introduction of right-handed neutrinos to the existence and stability of dark matter by a new U(1) gauge symmetry for dark photon or baryon-minus-lepton number. We then specify how to embed our scenario into a left-right symmetric theory or a grand unification theory.