The capacity to predict X-ray transition and K-edge energies in dense finite-temperature plasmas with high precision is of primary importance for atomic physics of matter under extreme conditions. The dual characteristics of bound and continuum states in dense matter are modeled by a valence-band-like structure in a generalized ion-sphere approach with states that are either bound, free, or mixed. The self-consistent combination of this model with the Dirac wave equations of multielectron bound states allows one to fully respect the Pauli principle and to take into account the exact nonlocal exchange terms. The generalized method allows very high precision without implication of calibration shifts and scaling parameters and therefore has predictive power. This leads to new insights in the analysis of various data. The simple ionization model representing the K-edge is generalized to excitation–ionization phenomena resulting in an advanced interpretation of ionization depression data in near-solid-density plasmas. The model predicts scaling relations along the isoelectronic sequences and the existence of bound M-states that are in excellent agreement with experimental data, whereas other methods have failed. The application to unexplained data from compound materials also gives good agreement without the need to invoke any additional assumptions in the generalized model, whereas other methods have lacked consistency.