The initial depressions of the superconducting transition temperature Tc of LaSn3 by rare earth (RE) impurities are known to be anomalous. In an attempt to clarify this behavior, we have measured the pressure dependence of the Tc of (LaRE)Sn3 alloys (RE = Y, Ce, Pr, Nd, Sm, Eu, Gd, and Lu) to pressures up to 25 kbar. The magnitude of the pressure dependence of the Tc of (LaRE)Sn3 alloys containing RE impurities with partially filled 4 f electron shells decreases monotonically with increasing RE atomic number. A general discussion of existing zero- and high-pressure data for various physical properties of (LaRE)Sn3 alloys demonstrates that the association of large pressure dependences of Tc with the occurrence of unstable impurity 4 f shells (the Kondo effect) should be made with caution. The experimental high-pressure results are analyzed in terms of appropriate theoretical models for magnetic and nonmagnetic localized impurity states in superconductors. © 1979 Plenum Publishing Corporation.