We consider an extension of the Standard Model with three right-handed (RH) neutrinos and a Dirac pair of extra sterile neutrinos, odd under a discrete Z(2) symmetry, in order to have left-right symmetry in the neutrino content and obtain tiny neutrino masses from the latter ones only. Our working hypothesis is that the heavy RH neutrinos do not influence phenomenology at low energies. We use the usual high-scale seesaw to suppress all of the mass terms involving RH neutrinos and a low-scale minimal variant of the linear seesaw led by the Dirac mass of the extra sterile neutrinos to provide the small mass of active neutrinos. One of the active neutrinos is massless, which fixes the mass of the other two on the basis of a soft breaking of the Z(2) symmetry. The mixing between the extra neutrinos makes for a particle that effectively behaves like a Dirac sterile neutrino with mass around the GeV level.