A novel, to the best of our knowledge, postprocessing technique is proposed to extract with a flexible and variable spatial resolution the information from Brillouin optical time-domain analyzers, obtained using a pulse longer than the acoustic settling time. The negative impact of the acoustic transient effect is suppressed, enabling a Brillouin response proportional to the spatial resolution and a Brillouin gain spectrum keeping its natural linewidth. This leads to a better overall sensing performance, in particular for submetric spatial resolutions, with no compromises on sensing range and measurement time.