•Demonstrate how NODDI outputs change when the assumed axial diffusivity is modified.•Combine high b-value data (to isolate intra-axonal signal) with dispersed stick model.•Simultaneously estimate the intra-axonal axial diffusivity and orientation dispersion.•Results from in vivo data show intra-axonal axial diffusivity in range 2-2.5 µm2/ms.•Simulations demonstrate importance of incorporating noise characteristics in low SNR regime. To estimate microstructure-related parameters from diffusion MRI data, biophysical models make strong, simplifying assumptions about the underlying tissue. The extent to which many of these assumptions are valid remains an open research question. This study was inspired by the disparity between the estimated intra-axonal axial diffusivity from literature and that typically assumed by the Neurite Orientation Dispersion and Density Imaging (NODDI) model (d∥=1.7μm2/ms). We first demonstrate how changing the assumed axial diffusivity results in considerably different NODDI parameter estimates. Second, we illustrate the ability to estimate axial diffusivity as a free parameter of the model using high b-value data and an adapted NODDI framework. Using both simulated and in vivo data we investigate the impact of fitting to either real-valued or magnitude data, with Gaussian and Rician noise characteristics respectively, and what happens if we get the noise assumptions wrong in this high b-value and thus low SNR regime. Our results from real-valued human data estimate intra-axonal axial diffusivities of ∼2−2.5μm2/ms, in line with current literature. Crucially, our results demonstrate the importance of accounting for both a rectified noise floor and/or a signal offset to avoid biased parameter estimates when dealing with low SNR data.