The effect of externally applied pressure on the magnetic behavior of Cu2 Te2 O5 (Brx Cl1-x) 2 with x=0, 0.73, and 1, is investigated by a combination of magnetic susceptibility, neutron diffraction, and neutron inelastic scattering measurements. The magnetic transition temperatures of the x=0 and 0.73 compositions are observed to increase linearly with increasing pressure at a rate of 0.23(2) and 0.04(1) K kbar, respectively. However, the bromide shows contrasting behavior with a large suppression of the transition temperature under pressure, at a rate of -0.95(9) K kbar. In neutron inelastic scattering measurements of Cu2 Te2 O5 Br2 under pressure only a small change to the ambient pressure magnetic excitations were observed. A peak in the density of states was seen to shift from ∼5 meV in ambient pressure to ∼6 meV under an applied pressure of 11.3 kbar, which was associated with an increase in the overall magnetic coupling strength. © 2006 The American Physical Society.