Significant progress in the theoretical description of Mott-Hubbard metal-to-insulator transitions has been made in the last years, especially thanks to the LDA+DMFT approach (local density approximation + dynamical mean field theory). Obviously the main attention has been focused on the transition itself, as, for example, in the textbook case of the Cr-doped V2O3. As we discuss here, however, also the study of the insulating phase, characterized by the opening of a visible Mott-Hubbard gap in the spectral functions is far from being trivial: Strong-correlation effects make this phase strongly sensitive to small changes of external parameters, much more than one would expect for an insulator. In this situation, requiring a full consistency of the theoretical calculations with data from different spectroscopies may provide the most precise estimate for the local Coulomb interaction U in the LDA+DMFT approach.