We investigate the gain bandwidth of stimulated Brillouin scattering (SBS) in multistage systems. As we will show, the bandwidth is reduced significantly by the number of stages, which can increase the distortions in cascaded slow-light systems, for instance. However, other applications, which are limited by the minimum bandwidth achievable with SBS, can benefit from the reduced bandwidth. Since the peak value of the SBS gain spectrum is not reduced by this method, the reduced bandwidth can drastically enhance the performance of many different applications, such as the quasi-light storage (QLS). The minimum bandwidth of 10.3 MHz for a one-stage system was reduced down to 5.8 MHz for three stages. With this reduced bandwidth, we achieved a storage time advancement of the QLS method by 60%.