The high-frequency Floquet theory (HFFT) of laser-atom interactions solves the space-translated version of the Schrödinger equation by an iterative procedure, leading to corrections of increasing order in the inverse photon energy. The lowest-order approximation (high-frequency limit) has been often evaluated before, but its accuracy at finite frequencies has not been established. To explore this issue we have computed the corrections yielded by the first-order iteration to the energy levels, and the ionization rates of a one-dimensional atomic model with a Gauss attractive potential. We have then compared, at frequencies above the field-free ionization potential |W0|, the HFFT results with those of a full Floquet calculation. We show that the agreement is substantially improved by the inclusion of the HFFT corrective terms. The agreement is good at all intensities for photon energies larger than several times |W0|. Even when the photon energy is marginally larger than |W0| the discrepancies vanish at sufficiently high intensities.