Enhanced degrees of nuclear polarization have been achieved by dynamic methods involving saturation of radiation-induced transitions between the various pairs of magnetic energy levels of an electron-nuclear coupled spin system (I). The conventional methods include the Overhauser effect (2) involving saturation of the allowed electron paramagnetic (AV = & 1, Am = 0) transitions and the Jefbies-Abragam effect (3) involving saturation of the first-order forbidden flip-flop (hM = f 1, Am = T 1) transitions. Obviously the weaker transitions have not been employed as the saturation of such transitions in an experiment becomes enormously difficult. The present paper suggests another spin-pumping scheme for obtaining enhanced nuclear polarization. It involves the saturation of AiW = +2, Am = Tl transitions which under the assumed conditions are seen to be comparable, in strength, to the first-order forbidden flip-flop transitions. The value of nuclear polarization expected in an experiment employing this spin-pumping scheme is found to be higher than those attainable by the conventional methods for the same values of the externally applied static magnetic field and temperature. The calculations apply to paramagnetic ions having nuclear spin Z = f and embedded in an axially symmetric environment as in crystals. The externally applied static magnetic field is assumed to be parallel to the crystal symmetry axis which is quite common in experimental setups. The terms of the spin Hamiltonian that have been taken into account are the electronic Zeeman, crystal field, and the hyperfme interaction. The nuclear Zeeman term has been neglected. The relevant spin Hamiltonian (4), under the above assumptions, is