The dependence of switching power upon input beam spot radius for an optically bistable InSb étalon has been measured. The results show that the irradiance required for switching increases as the spot radius is reduced. There is no evidence of any lower limit to the switching power, even for spot radii much less than the ambipolar diffusion length. Studies of the transmitted beam intensity profile in the near-field demonstrate the role of diffusion in our observations. The implications of our results for digital optical processing are briefly discussed.