It is well known that phonon-induced relaxation processes play a significant role in accelerating magnetization relaxation in the low-temperature regime. Unfortunately, many SIMs (single-ion magnets) suffer from being quenched by these mechanisms such that neither out-of-phase signals nor magnetization hysteresis can be readily observed. Nevertheless, because it involves molecular motions at low-frequency (low-energy) levels, methods for synthetically controlling this factor have not yet been addressed by chemists. In this study, we prepared a series of three compounds in which one contains a rigid chelating ligand, and the other two contain analogous ligands that can coordinate more liberally. To our surprise, compound 1, with a rigid chelating ligand, displayed promising SIM behavior with out-of-phase signals up to 11 K in a zero d.c. magnetic field at an a.c. frequency of 1000 Hz. The other two (2 and 3) with dangling ligands failed to show significant out-of-phase signals until an extra d.c. field was applied. The results of magnetization relaxation studies suggest that the phonon-induced relaxation processes play an essential role in 2 and 3, even at very low temperatures. Nevertheless, the rigid chelating ligand in 1 prevents the molecule from being involved in phonon-induced relaxation processes that seriously interfere with the magnetization relaxation up to 5.6 K. Therefore, we concluded that the presence of a rigid chelating ligand can efficiently change the phonon-induced relaxation processes at low temperatures.