A numerical and analytical study of the Raman instability in a homogeneous plasma is presented in which the pump has been modeled to include the effects of broad bandwidth and the induced spatial incoherence (ISI) method of beam smoothing. For a time-averaged homogeneous growth rate gammaBAR0 and a bandwidth sigma, there is a significant reduction in Raman backscattering when sigma greater-than-or-similar-to 2-gamma-0, for gammaBAR0(2) near threshold intensity. However, for gammaBAR0(2) very large compared to the threshold, neither ISI nor bandwidth affects Raman scattering.