We study, at LEP II and Next Linear Collider energies, Higgs production via the bremsstrahlung channel , with and , and the corresponding irreducible background, in the presence of hard photon radiation, both from the initial and the final state. We carry out an analysis that includes the computation of all the relevant contributions to the complete tree-level matrix element for and makes use of the one at leading order interfaced with electron structure functions. We concentrate on the case of mass degeneracy , for which next-to-leading electromagnetic contributions can modify the content of -pairs coming from H and Z decays. A brief discussion concerning the case is also given.