Measurements of myelination and indicators of myelination status in the preterm brain could be predictive of later neurological outcome. Quantitative imaging of myelin could thus serve to develop predictive biomarkers; however, accurate estimation of myelin content is difficult. In this work we show that measurement of the myelin water fraction (MWF) is achievable using widely available pulse sequences and state-of-the-art algorithmic modelling of the MR imaging. We show results of myelin water fraction measurement at both 30 (4 infants) and 40 (2 infants) weeks equivalent gestational age (EGA) and show that the spatial pattern of myelin is different between these ages. Furthermore we apply a multi-component fitting routine to multi-shell diffusion weighted data to show differences in neurite density and local spatial arrangement in grey and white matter. Finally we combine these results to investigate the relationships between the diffusion and myelin measurements to show that MWF in the preterm brain may be measured alongside multi-component diffusion characteristics using clinically feasible MR sequences.