Four new neutral copper-azido polymers [Cu₄(N₃)₈(Me-hmpz)₂]_n (1), [Cu₄(N₃)₈(men)₂]_n (2), [Cu₅(N₃)₁₀(N,N-dmen)₂]_n (3) and [Cu₅(N₃)₁₀(N,N′-dmen)₅]_n (4) [Me-hmpz = 1-methylhomopiperazine; men = N-methylethylenediamine; N,N-dmen = N,N-dimethylethylenediamine and N,N′-dmen = N,N′-dimethylethylenediamine] have been synthesized by using various molar equivalents of the chelating diamine ligands with Cu(NO₃)₂·3H₂O and an excess of NaN₃. Single-crystal X-ray structures show that the basic asymmetric units of 1 and 2 are very similar, but the overall 1D structures were found to be quite different. Complex 3 with a different composition was found to be 2D in nature, while the 1D complex 4 with 1 : 1 metal to diamine ratio presented several new structural features. Cryomagnetic susceptibility measurements over a wide range of temperature were corroborated with density functional theory calculations (B3LYP functional) performed on the complexes 1–3 to provide a qualitative theoretical interpretation of their overall magnetic behavior.