Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and microscopic diffusion anisotropy (i.e., the diffusion anisotropy expected for a single fibre orientation). This means that estimates of fibre dispersion rely on strong assumptions, such as constant microscopic anisotropy throughout the white matter or specific biophysical models. Here we present a simple approach for resolving this degeneracy using measurements that combine linear (conventional) and spherical tensor diffusion encoding. To test the accuracy of the fibre dispersion when our microstructural model is only an approximation of the true tissue structure, we simulate multi-compartment data and fit this with a single-compartment model. For such overly simplistic tissue assumptions, we show that the bias in fibre dispersion is greatly reduced (~5x) for single-shell linear and spherical tensor encoding data compared with single-shell or multi-shell conventional data. In in-vivo data we find a consistent estimate of fibre dispersion as we reduce the b-value from 3 to 1.5 ms/μm2, increase the repetition time, increase the echo time, or increase the diffusion time. We conclude that the addition of spherical tensor encoded data to conventional linear tensor encoding data greatly reduces the sensitivity of the estimated fibre dispersion to the model assumptions of the tissue microstructure.