Two series of heterometallic LnIII-CuII compounds containing a butterfly-like tetranuclear metal core were synthesized and characterized by X-ray diffraction and magnetometry. The structures of the new compounds were shown to depend on the nature of the hydroxide used for the synthesis. The reactions of copper(II) and lanthanide(III) salts with Hpiv (Hpiv is trimethylacetic acid) and LiOH in a MeCN-EtOH mixture afford the molecular complexes [Ln2Cu2(μ3-OH)2(piv)8(H2O)4]·4EtOH (1Ln, Ln = Gd, Tb, Dy, Ho, Yb), whereas the similar reactions using NaOH instead of LiOH give the 1D coordination polymers [Na2Ln2Cu2(μ3-OH)2(piv)10(EtOH)2]·EtOH (2Ln, Ln = Gd, Tb, Dy, Ho, Yb). According to ac susceptibility measurements, the DyIII-CuII compounds (1Dy and 2Dy) exhibit slow relaxation of magnetization indicative of single-molecule magnet (SMM) behavior. In the series of YbIII-CuII compounds, only complex 2Yb shows frequency-dependent out-of-phase ac susceptibility signals. This is the first reported example of carboxylate-based YbIII-CuII compound displaying slow magnetic relaxation.