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We consider scattering of x rays by H atoms in the presence of both a linearly polarized laser field and a static electric field. Results for the differential cross section as a function of the number of photons n exchanged with the laser field are presented. For x-ray–atom scattering in the presence of a 1014 W/cm2 laser field the differential cross section has a plateau only for emitted photons (n<0). Adding a static electric field gives rise to an extended plateau for absorbed photons (n>0), indicating a substantial increase of the scattered x-ray energies. We present a quasiclassical explanation of these results.