Purpose: To allow efficient extraction of NODDI parameters from data intended for DTI analysis, permitting biophysical analysis of DTI datasets. Theory: Simple relations between NODDI parameters (representing axon density, ν, and dispersion, τ ) and DTI invariants (MD and FA) were derived through moment expansion of the NODDI signal model with no CSF compartment. NODDI-DTI uses these relations to extract NODDI parameters from DTI data. Diffusional kurtosis strongly biased MD estimates, thus a novel heuristic correction requiring only DTI data was derived and used. Methods: NODDI-DTI parameter estimates using the first shell of data were compared to parameters extracted by fitting the NODDI model to (i) both shells (recommended) and (ii) the first shell (as for NODDI-DTI) of data in white matter of three different in vivo datasets, with CSF volume fraction fixed at zero. Results: NODDI-DTI and one-shell NODDI parameter estimates gave similar errors compared to two-shell NODDI estimates. NODDI-DTI gave unphysical parameter estimates in a small percentage of voxels, reflecting voxelwise DTI estimation error or NODDI model invalidity. Conclusion: NODDI-DTI is a promising technique to interpret restricted datasets acquired for DTI analysis biophysically, though its limitations must be borne in mind.