Three new copper(II) complexes of formula [Cu(tppz)(NCO)₂]·0.4H₂O (1), [Cu₂(tppz)Br₄] (2) and [Cu₃(tppz)(C₅O₅)₃(H₂O)₃]·7H₂O (3) [tppz = 2,3,5,6-tetrakis(2-pyridyl)pyrazine; C₅O₅²⁻ = croconate, dianion of 4,5-dihydroxycyclopent-4-ene-1,2,3-trione] have been synthesised and structurally characterized by X-ray diffraction methods. The structure of complex 1 is made up of neutral [Cu(tppz)(NCO)₂] mononuclear units and uncoordinated water molecules. The mononuclear units are grouped by pairs to give a rather short copper–copper distance of 3.9244(4) Å. The structure of complex 2 consists of neutral tppz-bridged [Cu₂(tppz)Br₄] dinuclear units, the copper–copper separation across tppz being 6.6198(1) Å. The dinuclear units are further connected through weak, double out-of-plane Cu–Br⋯Cu bridges [Br(1)⋯Cu(1a) 4.0028(17) Å] creating tetranuclear entities, the copper–copper separation through this interaction being 4.3299(21) Å. The structure of complex 3 is built of neutral [Cu₃(tppz)(C₅O₅)₃(H₂O)₃] trinuclear units and uncoordinated water molecules. Tppz and one of the croconate groups act as bridging ligands, the former exhibiting the bis-terdentate coordination mode and the latter adopting an unusual asymmetrical bis-bidentate bridging mode through three adjacent oxygen atoms. The other two croconate groups exhibit the bidentate coordination mode. The intramolecular copper–copper separations are 6.5417(9) (across tppz) and 4.3234(9) Å (through bis-bidentate croconato). The magnetic properties of 2 and 3 have been investigated in the temperature range 1.9–300 K. The magnetic behaviour of complex 2 is that of an antiferromagnetically coupled copper(II) dimer (J = −40.9 cm⁻¹, the Hamiltonian being Ĥ = −JŜ_A·Ŝ_B). In the case of compound 3, the χ_MTvs. T plot is typical of an overall antiferromagnetic coupling with a low-lying spin doublet being fully populated at T < 10 K. The values of the intramolecular antiferromagnetic interactions in 3 are −19.9 (across tppz) and −32.9 cm⁻¹ (through bridging croconato). Density functional type calculations were performed on model dinuclear fragments of 3 in order to analyze the efficiency of the exchange pathways involved and also to substantiate the coupling parameters.