The rate of nuclear spin-lattice relaxation is determined by the efficiency of interaction between thermal phonons and nuclear spins. The results on reducing the efficiency of spin–phonon coupling by suppressing the contribution from paramagnetic centers to quadrupole nucleus relaxation are presented. The suppression has been performed by continuous magnetic action at the Larmor frequency. It is shown that, as in the presence of an acoustic field, the rate of spin-lattice relaxation of 23Na nuclei in a sodium fluoride crystal at magnetic saturation of the NMR signal does not change in the region of a negative average spin temperature. In the region of positive spin temperature, the rate of relaxation of 23Na spins significantly decreases and nuclear magnetization recovery with time is described by the sum of two exponentials. The contribution from nuclear spins with a lower efficiency of spin–phonon coupling, corresponding to the exponential with a long relaxation time, increases with increasing saturating field intensity. It is demonstrated that the efficiency of spin–phonon coupling for 19F nuclei, which do not have the quadrupole moment, does not change under the saturation conditions. The results obtained can be used for analyzing the structure of real crystals