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We investigate the dependence of the speed of recovery of optically excited semiconductor optical amplifiers (SOAs) on the active region dimensions. We use a picosecond pump-probe arrangement to experimentally measure and compare the gain and phase dynamics of four SOAs with varying active region dimensions. A sophisticated time domain SOA model incorporating amplified spontaneous emission (ASE) agrees well with the measurements and shows that, in the absence of a continuous wave (CW) beam, the ASE plays a similar role to such a holding beam. The experimental results are shown to be consistent with a recovery rate which is inversely proportional to the optical area. A significant speed increase is predicted for an appropriate choice of active region dimensions.