Polarized and unpolarized neutron-diffraction studies have been carried out on single crystals of the coupled spin tetrahedra systems Cu2 Te2 O5 X2 (X=Cl, Br). A model of the magnetic structure associated with the propagation vectors k′ Cl ≈ (-0.150,0.422, 1 2) and k′ Br (-0.172,0.356, 1 2) and stable below TN =18 K for X=Cl and TN =11 K for X=Br is proposed. A feature of the model, common to both the bromide and chloride, is a canted coplanar motif for the four Cu2+ spins on each tetrahedron which rotates on a helix from cell to cell following the propagation vector. The Cu2+ magnetic moment determined for X=Br,0.395(5) μB, is significantly less than for X=Cl,0.88(1) μB at 2 K. The magnetic structure of the chloride associated with the wave vector k′ differs from that determined previously for the wave vector k ≈ (0.150,0.422, 1 2) [O. Zaharko, Phys. Rev. Lett. 93, 217206(E) (2004)]. © 2006 The American Physical Society.