Synthesis, crystal structures and magnetic studies are reported for four new heterometallic Cu(II)-Ln(III) clusters. The reaction of Cu(NO(3))(2)·3H(2)O with triethanolamine (teaH(3)), pivalic acid, triethylamine and Ln(NO(3))(3)·6H(2)O (Ln=Gd, Tb, Dy and Ho) results in the formation of four isostructural nonanuclear complexes of general formula [Cu(II)(5)Ln(III)(4)O(2)(teaH)(4){O(2)CC(CH(3))(3)}(2)(NO(3))(4)(OMe)(4)]·2MeOH·2Et(2)O [Ln=Gd (1), Tb (2), Dy (3) and Ho (4)]. The metal core of each cluster is made up of four face- and vertex-sharing tetrahedral units. Solid-state DC magnetic susceptibility studies reveal competing anti- and ferromagnetic interactions within each cluster leading to large-spin ground states for 1-4. Solid-state AC magnetic susceptibility studies show frequency-dependent out-of-phase (χ''(M)) signals for 2-4 below 4 K, suggestive of single-molecule magnet behaviour. Ab initio calculations on one of the anisotropic examples (3) provided a rare set of J values for Dy-Cu and Cu-Cu exchange interactions (Dy-Dy zero), some ferro- and some antiferromagnetic in character, that explain its magnetic behaviour.