We present a comparative study of the coupled-tetrahedra quantum spin systems Cu 2 Te 2 O 5 X 2 , X=Cl, Br (Cu–2252(X)) and the newly synthesized Cu 4 Te 5 O 12 Cl 4 (Cu–45124(Cl)) based on ab initio density functional theory calculations. The magnetic behavior of Cu–45124(Cl) with a phase transition to an ordered state at a lower critical temperature T c =13.6K than in Cu–2252(Cl) (T c =18.2K) can be well understood in terms of the modified interaction paths. We identify the relevant structural changes between the two systems and discuss the hypothetical behavior of the not yet synthesized Cu–45124(Br) with an ab initio relaxed structure using Car–Parrinello molecular dynamics.