Decommissioning of old nuclear reactors may produce waste streams containing chlorides and carbonates, including radioactive 36Cl− and 14CO3 2−. Their insolubilization by calcium monosulfoaluminate hydrate was investigated. Carbonates were readily depleted from the solution, giving at thermodynamic equilibrium monocarboaluminate, monocarboaluminate+calcite, or calcite only, depending on the initial ratio between the anion and calcium monosulfoaluminate hydrate. Chloride ions reacted more slowly and were precipitated as Kuzel's salt, Kuzel's and Friedel's salts, or Friedel's salt only. Rietveld refinement of X-Ray powder diffraction patterns was successfully used to quantify the phase distributions, which were compared to thermodynamic calculations. Moreover, analysing the lattice parameters of Kuzel's salt as a function of its chloride content showed the occurrence of a restricted solid solution towards the sulfate side with general formula 3CaO*Al2O3*xCaCl2*(1−x)CaSO4*(12−2x)*H2O (0.36≤x≤0.50).