The shape of the electron energy spectrum in H-3 beta-decay permits a direct assay of the absolute scale of the neutrino mass; a highly accurate theoretical description of the electron energy spectrum is necessary to the empirical task. We update Sirlin's calculation of the outer radiative correction to nuclear beta-decay to take into account the non-zero energy resolution of the electron detector. In previous H-3 beta-decay studies the outer radiative corrections were neglected all together; only Coulomb corrections to the spectrum were included. This neglect artificially pushes m(nu)(2) < 0 in a potentially significant way. We present a computation of the theoretical spectrum appropriate to the extraction of the neutrino mass in the sub-eV regime. (C) 2004 Published by Elsevier B.V.