The space requirements of atoms are generally regarded as key constraints in the structures, reactivity, and physical properties of chemical systems. However, the empirical nature of such considerations renders the elucidation of these size effects with first-principles calculations challenging. DFT-chemical pressure (DFT-CP) analysis, in which the output of DFT calculations is used to construct maps of the local pressures acting between atoms due to lattice constraints, is one productive approach to extracting the role of atomic size in the crystal structures of materials. While in principle this method should be applicable to any system for which DFT is deemed an appropriate treatment, so far it has worked most successfully when semicore electrons are included in the valence set of each atom to supply an explicit repulsive response to compression. In this Article, we address this limiting factor, using as model systems intermetallics based on aluminum, a key component in many structurally interesting phases that is not amenable to modeling with a semicore pseudopotential. Beginning with the Laves phase CaAl2, we illustrate the difficulties of creating a CP scheme that reflects the compound's phonon band structure with the original method due to minimal core responses on the Al atoms. These deficiencies are resolved through a spatial mapping of three energetic terms that were previously treated as homogeneous background effects: the Ewald, E-alpha, and nonlocal pseudopotential components. When charge transfer is factored into the integration scheme, CP schemes consistent with the phonon band structure are obtainable for CaAl2, regardless of whether Ca is modeled with a semicore or valence-only pseudopotential. Finally, we demonstrate the utility of the revised method through its application to the La3Al11 structure, which is shown to soothe CPs that would be encountered in a hypothetical BaAl4 -type parent phase through the substitution of selected Al-2 pairs with single Al atoms. La3Al11 then emerges as an example of a more general phenomenon, CP-driven substitutions of simple motifs.