Three new closely related CoIIYIII complexes of general formula [Co(μ-L)(μ-X)Y(NO3)2] (X−=NO3 − 1, benzoate 2, or 9-anthracenecarboxylato 3) have been prepared with the compartmental ligand N,N′,N′′-trimethyl-N,N′′-bis(2-hydroxy-3-methoxy-5-methylbenzyl)diethylenetriamine (H2L). In these complexes, CoII and YIII are triply bridged by two phenoxide groups belonging to the di-deprotonated ligand (L2−) and one ancillary anion X−. The change of the ancillary bridging group connecting CoII and YIII ions induces small differences in the trigonally distorted CoN3O3 coordination sphere with a concomitant tuning of the magnetic anisotropy and intermolecular interactions. Direct current magnetic, high-frequency and -field EPR (HFEPR), frequency domain Fourier transform THz electron paramagnetic resonance (FD-FT THz-EPR) measurements, and ab initio theoretical calculations demonstrate that CoII ions in compounds 1–3 have large and positive D values (≈50 cm−1), which decrease with increasing the distortion of the pseudo-octahedral CoII coordination sphere. Dynamic ac magnetic susceptibility measurements indicate that compound 1 exhibits field-induced single-molecule magnet (SMM) behavior, whereas compounds 2 and 3 only display this behavior when they are magnetically diluted with diamagnetic ZnII (Zn/Co=10:1). In view of this, it is always advisable to use magnetically diluted complexes, in which intermolecular interactions and quantum tunneling of magnetism (QTM) would be at least partly suppressed, so that “hidden single-ion magnet (SIM)” behavior could emerge. Field- and temperature-dependence of the relaxation times indicate the prevalence of the Raman process in all these complexes above approximately 3 K.