We have further developed a QRPA model that uses single-particle levels and wave-functions as the starting point for calculating Gamow-Teller β-strength functions. In our enhanced version Nilsson, Woods-Saxon, or folded-Yukawa wave functions and single-particle energies may serve as the starting point for determining the wave functions of the mother and daughter nuclei involved in the β-decay. Pairing may be treated in either the BCS or the Lipkin-Nogami approximation. To account for the retardation of low-energy GT decay rates we add, as in the earlier model, a simple residual interaction specific to GT decay, namely VGT = : β1- · β1+:, to the hamiltonian. This residual interaction is studied in the RPA approximation. In the case of odd-mass nuclei the ∆ν = 0 transitions are generally treated in a first-order perturbation expansion. We found that these expansions occasionally break down, and have modified them to avoid the singularities. The odd-odd case is treated in a way analogous to the odd- A case by considering one or the other of the odd particles as a spectator for ∆ν = 0 and both as spectators for ∆ν = 2. As a final extension of the earlier model, we also allow the unpaired odd particle to be in an excited state. We use the enhanced model to calculate Gamow-Teller β-strength functions, β-decay half-lives, and β-delayed neutron emission probabilities for nuclei in several regions of the periodic system, but with the main emphasis on the rare-earth region.