The isostructural compounds of general formula Cu2Te2O5X2 (X = Cl, Br) have been synthesized by chemical transport reaction. They crystallize in the tetragonal system, space group P4̄ with a = 7.6209(3) Å, c = 6.3200(4) Å, and a = 7.8355(2) Å, c = 6.3785(2) Å for Cu2Te2O5Cl2 and Cu2Te2O5Br2 respectively. The three-dimensional network is built up by tetrahedral clusters of copper(II) in distorted square planar coordination, isolated in the [100] and [010] directions by [Te2O5E2] groups and in the [001] direction by [TeO3E] tetrahedra. This leads to what can be described as spin tubes in the [001] direction surrounded by large tunnels where 5s2 tellurium(IV) lone pairs and chlorine and bromine atoms interact. A careful analysis of the temperature dependence of the susceptibility reveals that even from the magnetic point of view, the building bricks are tetrahedra with all couplings roughly equivalent, and not squares with small diagonal couplings. These systems are thus expected to have very interesting magnetic properties, including a large singlet−triplet gap, and a band of singlet states inside this gap.