Magnetically dilute samples of complexes Dy(H(2)BPz(Me2)(2))(3) (1) and U(H(2)BPz(2))(3) (3) were prepared through cocrystallization with diamagnetic Y(H(2)BPz(Me2)(2))(3) (2) and Y(H(2)BPz(2))(3). Alternating current (ac) susceptibility measurements performed on these samples reveal magnetic relaxation behavior drastically different from their concentrated counterparts. For concentrated 1, slow magnetic relaxation is not observed under zero or applied dc fields of several hundred Oersteds. However, a 1:65 (Dy:Y) molar dilution results in a nonzero out-of-phase component to the magnetic susceptibility under zero applied dc field, characteristic of a single-molecule magnet. The highest dilution of 3 (1:90, U:Y) yields a relaxation barrier U(eff) = 16 cm(-1), double that of the concentrated sample. These combined results highlight the impact of intermolecular interactions in mononuclear single-molecule magnets possessing a highly anisotropic metal center. Finally, dilution elucidates the previously observed secondary relaxation process for concentrated 3. This process is slowed down drastically upon a 1:1 molar dilution, leading to butterfly magnetic hysteresis at temperatures as high as 3 K. The disappearance of this process for higher dilutions reveals it to be relaxation dictated by short-range intermolecular interactions, and it stands as the first direct example of an intermolecular relaxation process competing with single-molecule-based slow magnetic relaxation.