Complex tissue microstructure involving various types of cells and their membranes can deviate the movement of water molecules from the typical Gaussian diffusion. This deviation can be quantified using excess kurtosis to characterize tissue structural complexity. However, true kurtosis measurements can be obscured by complex white matter configurations such as fiber crossing, bending, and branching, which are ubiquitous in the brain. In this paper, we extend diffusion kurtosis imaging (DKI) to allow characterization of diffusional kurtosis in microstructural environments that are oriented heterogeneously. Our method, called microscopic DKI fits a cylindrically symmetric kurtosis model to the spherical mean of the diffusion signal as a function of diffusion weighting. The spherical mean, computed for each b-shell, is invariant to the fiber orientation distribution and is a function of per-axon microstructural properties. Experimental results indicate that DKI yields significantly higher consistency in quantifying microstructure than the conventional DKI in the presence of orientation heterogeneity.