We report measurements of one-, two-, and three-photon processes during the elastic scattering of electrons through 90 ∘ by helium, argon, and molecular-nitrogen targets, in the presence of 1.17-eV photons from a Nd:YAG laser. The incident energy of the electrons was 200 and 350 eV, and the linear polarization direction of the laser was parallel to the momentum transfer direction. Our measured free-free count rates for the three processes are target independent within the experimental uncertainties, perfectly consistent with the Kroll-Watson approximation, which assumes no interaction of the laser radiation with the target.