  We report the self-energy associated with RPA magnetic susceptibility in the
hole-doped Bi_2Sr_2CuO_6 (Bi2201) and the electron-doped Nd_{2-x}Ce_xCuO_4
(NCCO) in the overdoped regime within the framework of a one-band Hubbard
model. Strong weight is found in the magnetic spectrum around (pi, 0) at about
360 meV in Bi2201 and 640 meV in NCCO, which yields dispersion anomalies in
accord with the recently observed `waterfall' effects in the cuprates.
