We report an amine-free synthesis of lead halide perovskite (LHP) nanocrystals, using trioctylphosphine oxide (TOPO) instead of aliphatic amines, in combination with a protic acid (e.g., oleic acid). The overall synthesis scheme bears many similarities to the chemistry behind the preparation of LHP thin films and single crystals, in terms of ligand coordination to the chemical precursors. The acidity of the environment and hence the extent of protonation of the TOPO molecules tune the reactivity of the PbX2 precursor, regulating the size of the nanocrystals. On the other hand, TOPO molecules are virtually absent from the surface of our nanocrystals, which are simply passivated by one type of ligand (e.g., Cs-oleate). Furthermore, our studies reveal that Cs-oleate is dynamically bound to the surface of the nanocrystals and that an optimal surface coverage is critical for achieving high photoluminescence quantum yield. Our scheme delivers NCs with a controlled size and shape: only cubes are formed, with no contamination with platelets, regardless of the reaction conditions that were tested. We attribute such a shape homogeneity to the absence of primary aliphatic amines in our reaction environment, since these are known to promote the formation of nanocrystals with sheet/platelet morphologies or layered phases under certain reaction conditions. The TOPO route is particularly appealing with regard to synthesizing LHP nanocrystals for large-scale manufacturing, as the yield in terms of material produced is close to the theoretical limit: i.e., almost all precursors employed in the synthesis are converted into nanocrystals.