The effect of transmission through a fiber Bragg grating on the relative intensity noise of semiconductor laser light is investigated. We first present a model of the grating as a linear frequency discriminator that exchanges correlated power between frequency noise and intensity noise caused by spontaneous emission. This correctly explains observed increases in intensity noise of up to 30 dB at low frequencies, obeying an inverse-square frequency dependence. Next, we show that there exist conditions under which a grating can reduce intensity noise and that these are determined by the phase relationship between correlated intensity and frequency fluctuations. Finally, we demonstrate a 2 dB reduction of intensity noise at frequencies up to 15 GHz, and present a numerical calculation based on the complex transmittance of the grating that correctly describes the effect of grating dispersion. ©1997 American Institute of Physics.