A non-empirical fully ionic description, with the anion wavefunctions in their compressed but still spherically symmetrical states optimal for the crystal, is presented for the cohesive energetics of two cubic phases of three solid iodides, KI, RbI and CsI. The non-correlated part of the energy is computed using the RELCRION program which takes full account of relativistic effects. Both the dispersive attractions and energies arising from electron correlations of short range are computed.For each polymorph stable under ambient conditions, the rock-salt (B1) phases of KI and RbI and the eightfold coordinated (B2) phase of CsI, the cohesion is slightly underestimated. The lattice energy deficits of around 22 kJ mol −1 for KI and RbI are reduced to around 13 kJ mol −1 for CsI, with overestimations of some 0.2 au in the equilibrium cation-anion separations R decreasing as the metal becomes more electropositive. The prediction that the B2 phase of CsI is more stable (by 6 kJ mol −1 ) than the B1 polymorph agrees with experiment. For both KI and RbI, the zinc-blende polymorph is predicted to lie some 37 kJ mol −1 in energy above the B1 polymorph.An additional potential, plausibly ascribed to slight covalency, correcting these underestimations is derived semi-empirically.