Physical reasons are presented for the coherent potential approximation (CPA) calculation method’s abillity to predict little band gap bowing or alloy scattering, while at the same time predicting large deviation from virtual crystal behavior in other energy ranges. Accurate treatment of structural properties requires that calculations be doubly self‐consistent: a density functional method plus CPA is needed. Experimental values of bond energies are greater than those predicted by simple theories. Weakened HgTe bonds in alloys help to explain the loss of Hg when the materials undergo surface treatments.