We investigate the influence of the excitation spot diameter on the laser threshold of a scattering amplifying medium. Fluorescence spectra are recorded from a suspension of TiO(2) scatterers in Sulforhodamine B dye. The threshold pump intensity becomes larger by a factor of 70 if the excitation beam diameter gets close to the mean free path?. This increase is explained by use of a simple model describing diffusion out of the amplifying volume and is confirmed by a Monte Carlo simulation.