We study numerically the photoionization of a one-dimensional model atom, with a very-short-range potential, in the Kramers-Henneberger frame. In the range where suppression of ionization is found, the ground-state depletion follows a well-fitted exponential decay. The decay rate has been examined for different values of the laser frequency and for different intensities. Comparisons with existing analytical predictions are made where appropriate. © 1993 The American Physical Society.