Clinically oriented studies commonly acquire diffusion MRI (dMRI) data with a single non-zerob-value (i.e. single-shell) and diffusion weighting ofb= 1000 s mm-2. To produce microstructural parameter maps, the tensor model is usually used, despite known limitations. Although compartment models have demonstrated improved fits in multi-shell dMRI data, they are rarely used for single-shell parameter maps, where their effectiveness is unclear from the literature. Here, various compartment models combining isotropic balls and symmetric tensors were fitted to single-shell dMRI data to investigate model fitting optimization and extract the most information possible. Full testing was performed in 5 subjects, and 3 subjects with multi-shell data were included for comparison. The results were tested and confirmed in a further 50 subjects. The Markov chain Monte Carlo (MCMC) model fitting technique outperformed non-linear least squares. Using MCMC, the 2-fibre-orientation mono-exponential ball and stick model (BSME2) provided artifact-free, stable results, in little processing time. The analogous ball and zeppelin model (BZ2) also produced stable, low-noise parameter maps, though it required much greater computing resources (50 000 burn-in steps). In single-shell data, the gamma-distributed diffusivity ball and stick model (BSGD2) underperformed relative to other models, despite being an often-used software default. It produced artifacts in the diffusivity maps even with extremely long processing times. Neither increased diffusion weighting nor a greater number of gradient orientations improvedBSGD2fits. In white matter (WM), the tensor produced the best fit as measured by Bayesian information criterion. This result contrasts with studies using multi-shell data. However, in crossing fibre regions the tensor confounded geometric effects with fractional anisotropy (FA): the planar/linear WM FA ratio was 49%, whileBZ2andBSME2retained 76% and 83% of restricted fraction, respectively. As a result, theBZ2andBSME2models are strong candidates to optimize information extraction from single-shell dMRI studies.