In Paranicas et al. (2020), we reported on a method to estimate the inflow speed of interchange injections in Saturn's magnetosphere. The procedure relies on phase space density conservation and mapping and an estimate of the size of the flux decrease along one edge of the injection. Here we describe modifications to the method. We have applied our new technique to an existing list of injections, presenting only those injections with inflow speeds greater than 20 km/s, defined as "fast" injections here. We find at least 20% of the events from the list can be considered fast. Faster injections are more effective in energizing charged particles as the injection moves planetward. This is because shorter transit time limits the number of particles that can drift longitudinally out of the injection.