Diffusion-weighted magnetic resonance imaging can be used to estimate microstructural parameters of white matter in the brain. Two complementary techniques are investigated: the use of the temporal diffusion spectrum to explore small length scales and the STEAM technique to probe larger features. The diffusion spectrum has the potential to be more sensitive to small pores compared to conventional time-dependent diffusion. However, analytical expressions for the diffusion spectrum of particles only exist for simple geometries such as cylinders, which are often used as a model for intra-axonal diffusion. We propose a mathematical model for the extra-axonal space with parameters that are related to the microstructural properties of pore size, tortuosity, and surface-to-volume ratio. Measurements were made with an extra-axonal space phantom to validate the model. Fitted values for the phantom pore size match those from simulation. We extend the model to include the intra-axonal signal contribution. However, the parameters used to describe the intra- and extra-axonal spaces are related and it is important to remove redundant parameters to avoid overparameterization, which would make the model less robust. We propose analytical expressions to simplify the model. The model was then applied to measurements on fixed corpus callosum, which is a model system consisting of parallel axons. The estimated values of the axon volume fraction and mean and standard deviation of the axon radius distribution are comparable to those found in literature. Temporal diffusion spectra are useful for measuring the geometric properties of small spaces such as axon radii. However, longer diffusion times accessible using the STEAM sequence are necessary to probe structures with longer diffusion distances such as those parallel to the direction of axons. We used a model from the literature originally developed for use with animal magnetic resonance scanners and simplified it to quantify axial hindrance from data acquired on healthy volunteers in a clinical scanner. The interpretation of axial hindrance, which is a largely unexplored area of research, is discussed.