A survey is made of different ways in which nuclear spins can relax through their interaction with electronic spins. It is shown that the maximum amount of nuclear polarization which can be obtained by saturating the electronic resonance depends: (a) on the type of interaction between electronic and nuclear spins, namely dipole-dipole type, scalar product type, or any combination of the two; (b) on the mechanism whereby the "lattice" provides the energy for the relaxation.The case of a nucleus belonging to a paramagnetic ion is examined in some detail with reference to the recent experiment of Honig on arsenic-doped silicon. It is shown that while an Overhauser effect may be expected, this offers no support for an interpretation of Honig's results as a hundred percent nuclear polarization.