The application of a picosecond-pulsed laser system, in conjunction with a time-to-amplitude converter, to the suppression of fluorescence noise in Raman spectra is described. Enhancements of 14.6 (Raman signal/fluorescence background) and 2.8 (Raman signal/fluorescence noise) were obtained for a solution of benzene doped with a fluorophore with lifetime tau _f=11.8 ns, while corresponding improvements of 5.5 and 2.0 were observed for a dopant with tau _f=3.9 ns. When the samples studied exhibited non-Poisson fluctuations in background intensity, the signal-to-noise enhancement was much greater (7.2). Calculations are presented which successfully model the signal-to-noise enhancement as a function of tau _f and the detector timing resolution. These calculations have been verified experimentally over a wide range of gate widths and positions. The importance of the Raman signal/fluorescence noise ratio rather than the Raman signal/fluorescence background level is stressed.