We report the results of the investigation of three phase diagrams: (i) CuO-CuCl2-SeO2, (ii) CuO-CuCl2/CuBr2-TeO2 and (iii) CuO-CuCl2/CuBr2-SeO2-Bi2O3. Four compounds have been isolated Cu-3(SeO3)(2)Cl-2, Cu9O2(SeO3)(4)Cl-6, Cu2Te2O5X2 (X = Cl, Br) and Cu3Bi(SeO3)(2)O2X (X = Cl, Br). Interesting structural arrangements are observed for the latter two: tetrahedral clusters of copper(II) ions for Cu2Te2O5X2 and copper(II)-oxygen layers of hexagonal shape made of [CuO4] square planes sharing apices whose geometry is reminiscent of a kagome type lattice. These compounds provide good experimental realizations of S = 1/2 low-dimensional 1D and 2D magnetic materials. The analysis of the magnetic susceptibility of Cu2Te2O5X2 reveals that the bricks are effectively tetrahedra with all couplings roughly equivalent; J(1) = J(2) with J(1) = 38.5 K for the chlorine compound and J(1) = 43 K for the bromine one. For Cu3Bi(SeO3)(2)O2Cl, a striking behavior is observed like, for instance, an absence of Cu2+ spin resonance at v = 9.44 GHz.