Abstract Diffusion kurtosis imaging (DKI) is being increasingly reported to provide sensitive biomarkers of subtle changes in tissue microstructure. However, DKI also imposes larger data requirements than diffusion tensor imaging (DTI), hence, the widespread adaptation and exploration of DKI would benefit from more efficient acquisition and computational methods. To meet this demand, we recently developed a method capable of estimating mean kurtosis with only 13 diffusion weighted images. This approach was later shown to provide very accurate mean kurtosis estimates and to be more efficient in terms of contrast to noise per unit time. However, insofar, the computation of two other critical DKI parameters, radial and axial kurtosis, has required the estimation of all 22 variables parameterizing the full DKI signal expression. Here, we present two strategies for estimating all of DKI's principal parameters – mean kurtosis, radial kurtosis, and axial kurtosis – using only 19 diffusion weighted images, compared to the current state-of-the-art acquisitions typically requiring about 60 images. The first approach is based on axially symmetric diffusion and kurtosis tensors, presented here for the first time, and referred to as axially symmetric DKI. The second approach is applicable in tissues with a priori known principal diffusion direction, and does not require fitting of any kind. The approaches are evaluated in human brain in vivo as well as in fixed rat spinal cord, and are demonstrated to provide metrics in good agreement with their full DKI counterparts estimated with nonlinear least squares. For small data sets and in white matter, axially symmetric DKI provides more accurate and robust estimates than unconstrained DKI. The significant acceleration achieved further paves the way to routine application of the technique.