Using the QCD sum rule approach, we calculate the electric dipole moments of the&rgr;+meson and the neutron induced by a vacuum &thgr;-angle to approximately 40–50&percent; precision. In the latter case, we finddn=1.2×10−16&thgr;˜e⋅cm,which combined with the new experimental bound, translates into the limit|&thgr;¯|<6×10−10.©1999 American Institute of Physics.