The dependence of the stimulated Brillouin scattering (SBS) reflectivity on both the focusing aperture and the incident laser intensity has been experimentally studied in the case of a spatially smoothed beam. The experiment was performed in millimeter size, homogeneous, stationary plasmas created by irradiating a helium gas jet. SBS was excited by a 1.053-\ensuremath{\mu}m wavelength, 600-ps interaction beam at intensities up to $4\ifmmode\times\else\texttimes\fi{}{10}^{14} {\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}.$ The saturation level of SBS reflectivities was of the order of 10%. A good agreement between the experimental SBS thresholds and the theoretical ones obtained from the one-dimensional stochastic convective SBS model [Phys. Plasmas 2, 1804 (1995)] is observed.