In many amplification regimes, the EDFA gain is saturated by noise. This is particularly true for in-line and preamplifier EDFA. The accurate computation of noise spectra is necessary to predict the EDFA exact gain and noise characteristics. In most cases, this is done by solving the rates equations describing the noise spectra. An interesting approach of noise unsaturated EDFA has been given by E. Desurvire. One ordinary differential equation (ODE) describes the whole noise spectrum in one direction. This is the usual concept of noise effective bandwidth (NEB). A set of 4 ODE is then required to compute gain and noise characteristics, leading to short computation times as a small size ODE system is concerned. The NEB definition we used has been modified in order to take into account the spatial distribution of the light power in the active fiber section and the population inversion. The NEB method we propose uses 1, 2, or 4 NEB, leading to small computation times (approximately equals 4s.). In order to generalize the results obtained by our method, several cases have been investigated: input signal powers of -40, -20, O dBm and input pump powers ranging from 10 to 30 mW. The worst case is the low input signal power because of the high noise level saturating the EDFA gain. The predictions provided by one modified NEB are at least better than the results obtained with 4 standard NEB, as defined by E. Desurvire. The computations fairly agree with the reference solution (integration of the rate equations): the larger discrepancy is lower than 0.7 dB.