In first approximation the binding of an electron in lanthanide 4fq ground states changes with q in a characteristic zigzag shape that is independent on type of compound. Those shapes have been parameterized in past publications and are used to construct host referred binding energy (HRBE) or vacuum referred binding energy (VRBE) schemes showing the lanthanide 4fq level locations with respect to the host valence bands or to the vacuum level. There is experimental evidence for a slight compound dependence, and a model explaining that has appeared recently (Dorenbos, 2019). This all implies that the parameters for constructing HRBE and VRBE schemes need to be revised and a compound dependence needs to be introduced as a second order approximation. In this work the improved parameters are derived from the 3rd and 4th ionization potentials of the lanthanide atoms. In compounds, as explained by the chemical shift model, the free ion binding energy curves undergo an upward shift due to Coulomb repulsion from anion ligands and they undergo a tilt due to the lanthanide contraction. In this work we will use the nephelauxetic parameter β to add a compound dependence. Its main effect is an increased binding in the 4fq ground states for the lanthanides from the right hand branch (q > 7) of the zigzag curves. The same applies for the 4fq−15d excited states with (q−1)>7. Collected spectroscopic data on divalent and trivalent lanthanides from more than 1000 different compounds have been analyzed to arrive at the proposed revised parameters for the 4fq and 4fq−15d binding energy curves.