The P 3 0 → D 1 2 non-radiative decay rates A N R of Pr 3 + and the transition probabilities A V I B for the vibronic H 3 4 → P 3 0 excitation transitions of Pr 3 + were measured at 4.2 K for Pr 3 + in several host lattices, ranging from hosts where the non-radiative decay is negligible (e.g. LiYF 4 :Pr, A N R = 50 s - 1 ) to hosts where it dominates (e.g. Lu 2 O 3 :Pr, A N R 10 7 s - 1 ). The compounds investigated can be divided into two groups concerning the order of the multiphonon relaxation: 6-7 and 4-5 phonons. 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 A V I B in the same sequence as the A N R rates. The observed host lattice dependence of A N R can be qualitatively accounted for by a nonlinear multiphonon relaxation mechanism. Under certain conditions (viz. low-lying 4f5d states, and a force constant stronger in the 4f5d state than in the 4f 2 states) fast P 3 0 → D 1 2 non-radiative relaxation via the 4f5d state becomes the dominant relaxation mechanism, even at 4.2 K.