The contributions of different mechanisms of nuclear spin-lattice relaxation are experimentally separated for ⁶⁹Ga and ⁷¹Ga nuclei in GaAs crystals (nominally pure and doped with copper and chromium), ²³Na nuclei in a nominally pure NaCl crystal, and ²⁷Al nuclei in nominally pure and lightly chromium-doped Al₂O₃ crystals in the temperature range 80-300 K. The contribution of impurities to spin-lattice relaxation is separated under the condition of additional stationary saturation of the nuclear magnetic resonance (NMR) line in magnetic and electric resonance fields. It is demonstrated that, upon suppression of the impurity mechanism of spin-lattice relaxation, the temperature dependence of the spin-lattice relaxation time T₁ for GaAs and NaCl crystals is described within the model of two-phonon Raman processes in the Debye approximation, whereas the temperature dependence of T₁ for corundum crystals deviates from the theoretical curve for relaxation due to the spin-phonon interaction.