SIR-MIR and SIRAS-MIRAS cases are studied by application of the joint probability distribution method. The final results are conditional probability distributions of the protein phases given the structure-factor moduli of the protein and of the derivatives, and the structure factors of the heavy-atom substructures. The approach is able to treat errors arising from measurements, from the heavy-atom structure model and from the lack of isomorphism. The relations between the present approach and previous methods are described. The formulas have been implemented in a procedure that is able to automatically phase protein reflections up to protein resolution [Giacovazzo, Ladisa & Siliqi (2002). Acta Cryst. A58, 598-604].