The effects of ultra high intensity laser radiation on dynamical processes such as electron scattering, bremsstrahlung emission, pair production, etc. have recieved growing theoretical interest as laser intensities in the laboratory continue to increase. Recently, for example, a calculation was published that predicted more than four orders of magnitude resonant increases in bremsstrahlung emission in the presence of intense optical laser radiation [A. A. Lebed and S. P. Roshchupkin, Phys. Rev. A, 81, 033413 (2010)]. The analysis in this paper was limited to laser intensities ≤ 10 17 W/cm 2 , and it was applied only to bremsstrahlung emissions at the laser frequency. In the present paper, we extend this Lebed and Roshchupkin analysis in order to assess the possibility of achieving some enhancement to bremsstrahlung emissions at significantly higher harmonics of the optical laser photon energies (∼ 6 keV) and thereby to appraise whether or not enhanced extensions of these calculations (or experimental measusurements) are needed to detemine whether the enhancement factors that are predicted for small laser harmonics at laser intensities < ∼ 10 17