This study uses Monte Carlo simulations to investigate the optimal value of the diffusion weighting factor b for estimating white-matter fiber orientations using diffusion MRI with a standard spherical sampling scheme. We devise an algorithm for determining the optimal echo time, pulse width, and pulse separation in the pulsed-gradient spin-echo sequence for a specific value of b. The Monte Carlo simulations provide an estimate of the optimal value of b for recovering one and two fiber orientations. We show that the optimum is largely independent of the noise level in the measurements and the number of gradient directions and that the optimum depends only weakly on the diffusion anisotropy, the maximum gradient strength, and the spin-spin relaxation time. The optimum depends strongly on the mean diffusivity. In brain tissue, the optima we estimate are in the ranges [0.7, 1.0] x 10(9) s m(-2) and [2.2, 2.8] x 10(9) s m(-2) for the one- and two-fiber cases, respectively. The best b for estimating the fractional anisotropy is slightly higher than for estimating fiber directions in the one-fiber case and slightly lower in the two-fiber case. To estimate Tr(D) in the one-fiber case, the optimal setting is higher still. Simulations suggest that a ratio of high to low b measurements of 5 to 1 is a good compromise for measuring fiber directions and size and shape indices.