Recording RBS spectra at the fastest possible rate presents obvious advantages. Speed is, moreover, a must when RBS is carried out simultaneously with NRA, when high-Z thick targets are analyzed, like YBaCuO, and a very large number of pulses must be processed for recording with sufficient statistics the narrow high-energy region of interest, when kinetics measurements are carried out in situ, the total time available for the measurements being limited by the physical process under study, etc. We present here the first results of a systematic search for increasing counting rates in RBS while keeping pileup-induced spectrum distortions within acceptable levels. The pileup-handling properties of the fastest available spectroscopy amplifiers were characterized. A probabilistic model was developed of the residual pileup process due to the pairs of pulses not resolved by the pileup rejection system. The corresponding algorithm implemented with the GENPLOT program with RUMP input-output format may be used to clean up the spectra from the residual pileup. We present examples of spectra recorded with counting rates up to 43 000 counts/s and treated successfully with this algorithm. The still unsolved problems and possible remedies are discussed.