This work shows that multi-fibre reconstruction techniques, such as Persistent Angular Structure (PAS) MRI or QBall Imaging, provide much more information than just discrete fibre orientations, which is all that previous tractography algorithms exploit from them. We show that the shapes of the peaks of the functions output by multiple-fibre reconstruction algorithms reflect the underlying distribution of fibres. Furthermore, we show how to exploit this extra information to improve Probabilistic Index of Connectivity (PICo) tractography. The method uses the Bingham distribution to model the uncertainty in fibre-orientation estimates obtained from peaks in the PAS or QBall Orientation Distribution Function (ODF). The Bingham model captures anisotropy in the uncertainty, allowing the method to track through fanning and bending structures, which previous methods do not recover reliably. We devise a new calibration procedure to construct a mapping from peak shape to Bingham parameters. We test the accuracy of the calibration using a bootstrap experiment. Finally, we show that exploiting the peak shape in this way can provide improved PICo tractography results.