This work proposes a revision of the NODDI model to relate brain tissue microstructure to the new generation of diffusion MRI data with multiple b-tensor encodings. NODDI was developed originally for conventional multi-shell diffusion data acquired with linear tensor encoding (LTE). While adequate for LTE data, it has been shown to be incompatible with data using spherical tensor encoding (STE). We embed a different set of assumptions in NODDI, while retaining the tortuosity constraint, to accommodate both LTE and STE data. Experiments with human data with multiple b-tensor encodings confirm the efficacy of the revision.