It is common to use the electron density to partition a system into atomic regions. The necessity for such a partitioning scheme is rooted in the unquestionable role of atoms in chemistry and chemical modeling. Nevertheless, atomic properties are not well-defined concepts within the domain of quantum mechanics as they are not physical observables. One of the most popular families of atoms-in-molecules models is the Hirshfeld partitioning scheme. The various flavors of the Hirshfeld scheme mainly differ in choosing the reference proatom density that is being used to define the fuzzy atomic densities. To address the ambiguity in selecting the reference proatom density, we introduce new methods for computing atomic densities within the additive variational Hirshfeld framework, in which the proatom density is defined as a convex linear combination of spherically averaged charged atomic electron densities. We focus in particular on dipole- and charge-constrained variants and evaluate their performance on chemically diverse datasets, with emphasis on reproducing electrostatic potentials, molecular moments, and electrostatic interactions. Our ultimate goal is to improve force-field models.