For a quantum-mechanical system and a given density, the Zhao-Morrison-Parr method allows to infer the effective potential that yields precisely this density. I will discuss how this can be understood as a limit procedure from Moreau-Yosida-regularized density functionals to the unregularized case. This sheds new insight on the relevance of regularization in density-functional theory and allows to systematically improve density-potential inversion. [mehr]