This report presents an investigation of composite fiber Raman amplifiers, i.e. a distributed fiber Raman amplifier followed by a discrete fiber Raman amplifier, both with incoherent pumping, compared to conventional coherent pumping. It is shown that a flatter gain and optical signal-to-noise ratio (OSNR) over 100-nm bandwidth can be achieved by using two incoherent counter-pumps, compared to using six coherent counter-pumps. Moreover, it is also found that further flatter gain and flatter OSNR over 100-nm bandwidth can be obtained simultaneously in composite fiber Raman amplifiers with bi-directional pumping. The flatness of both gain and OSNR with a ripple of 1 dB is predicted by using one incoherent co-pump and one incoherent counter-pump.