This study has investigated the relationship between the noise sensitivity of measurement by magnetic resonance imaging (MRI) of the diffusion tensor (D) of water and the number N of diffusion-weighting (DW) gradient directions, using computer simulations of strongly anisotropic fibers with variable orientation. The DW directions uniformly sampled the diffusion ellipsoid surface. It is shown that the variation of the signal-to-noise ratio (SNR) of three ideally rotationally invariant scalars of D due to variable fiber orientation provides an objective quantitative measure for the diffusion ellipsoid sampling efficiency, which is independent of the SNR value of the baseline signal obtained without DW; the SNR variation decreased asymptotically with increasing N. The minimum number N(0) of DW directions, which minimized the SNR variation of the three scalars of D was determined, thereby achieving the most efficient ellipsoid sampling. The resulting time efficient diffusion tensor imaging (DTI) protocols provide robust estimation of diffusion anisotropy in the presence of noise and can improve the repeatability/reliability of DTI experiments when there is high variability in the orientation of similar anisotropic structures, as for example, in studies which require repeated measurement of one individual, intersubject comparisons or multicenter studies.