Polarized and unpolarized neutron-diffraction studies have been carried out on single crystals of the coupled spin tetrahedra systems Cu2Te2O5X2 (X=Cl, Br). A model of the magnetic structure associated with the propagation vectors k(') (Cl) approximate to (-0.150,0.422, (1)/(2)) and k'(Br) approximate to (-0.172,0.356, (1)/(2)) and stable below T-N = 18 K for X= Cl and T-N = 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)mu(B), is significantly less than for X= Cl, 0.88 (1)mu(B) 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 approximate to (0.150,0.422, (1)/(2))