Purpose: Diffusion kurtosis imaging (DKI) is an advanced magnetic resonance imaging modality that is known to be sensitive to changes in the underlying microstructure of the brain. Image voxels in diffusion weighted images, however, are typically relatively large making them susceptible to partial volume effects, especially when part of the voxel contains cerebrospinal fluid. In this work, we introduce the “Diffusion Kurtosis Imaging with Free Water Elimination” (DKI-FWE) model that separates the signal contributions of free water and tissue, where the latter is modeled using DKI. Theory and Methods: A theoretical study of the DKI-FWE model, including an optimal experiment design and an evaluation of the relative goodness of fit, is carried out. To stabilize the ill-conditioned estimation process, a Bayesian approach with a shrinkage prior (BSP) is proposed. In subsequent steps, the DKI-FWE model and the BSP estimation approach are evaluated in terms of estimation error, both in simulation and real data experiments. Results: Although it is shown that the DKI-FWE model parameter estimation problem is ill-conditioned, DKI-FWE was found to describe the data significantly better compared to the standard DKI model for a large range of free water fractions. The acquisition protocol was optimized in terms of the maximally attainable precision of the DKI-FWE model parameters. The BSP estimator is shown to provide reliable DKI-FWE model parameter estimates. Conclusion: The combination of the DKI-FWE model with BSP is shown to be a feasible approach to estimate DKI parameters, while simultaneously eliminating free water partial volume effects.