A new methodology is introduced that characterizes the intravoxel orientation distribution function (ODF) based on a single-fiber model of the diffusion MRI signal. Using a Bayesian framework the probability of finding a fiber in a specific orientation is obtained. The proposed ODF estimation relies on a cigar-like diffusion tensor model, the methodology is thus denominated Bayesian cigar-like diffusion tensor (BCDT). This work makes two major contributions: 1) the study of single-fiber models in detecting fibers with different volume fractions in a voxel, and 2) the introduction of the Nth-root correction to improve the detection of fibers with smaller volume fractions, where N is the number of diffusion MRI measurements. It is demonstrated that the incomplete signal modeling fails to reconstruct the relative fiber volume fractions, especially when the intravoxel diffusion profiles have dissimilar contributions to the diffusion MRI signal. In this situation the fibers with smaller contributions are hardly detectable. The BCDT method proposed here reduces this effect by introducing the Nth-root correction, making multiple fibers estimable. The performance of the new methodology is illustrated using synthetic and real data, as well as the data from a phantom of intersecting capillaries.