Two recently introduced self-consistent Hirshfeld procedures for obtaining atoms in molecules are compared in detail. The Hirshfeld-I scheme introduces self consistency by requiring that the atomic population of the promolecular atom is equal to that of the atom-in-the-molecule. In the iterated stockholder atoms (ISA) approach, self consistency is obtained by requiring that for every value of the radius of a sphere around every nucleus, the average electron density on the surface of this sphere is the same in the promolecular atom and in the atom in the molecule. The relationships between the two schemes are examined, and common backgrounds and differences are discussed. Whereas it can be argued that the Hirshfeld-I approach has a stronger physical background, the ISA scheme avoids having to define what states of the atoms are to be considered when constructing the promolecule.