The3P0→1D2 non-radiative decay rates ANR of Pr3+ and the transition probabilities AVIB for the vibronic3H4→3P0 excitation transitions of Pr3+ were measured at 4.2 K in several host lattices. Besides the well-known dependence on the number of phonons involved in the radiationless transition, the multiphonon relaxation rates are observed to be greatly enhanced by increasing covalency and/or decreasing Pr-ligand distances. The enhanced multiphonon relaxation is ascribed to a stronger electron-phonon coupling. The increase in the electron-phonon coupling strength is confirmed by the increase of the vibronic transition probabilities AVIB in the same sequence as the ANR rates. The observed host lattice dependence of ANR can be qualitatively accounted for by a non-linear multiphonon relaxation mechanism. Under certain conditions (viz. low-lying 4f5d states, and a force constant stronger in the 4f5d than in the 4f2 states) fast3P0→1D2 non-radiative relaxation via intersystem crossing through the 4f5d state becomes the dominant relaxation mechanism, even at 4.2 K.