Method for purifying combustion fumes, characterised in that it comprises the following steps, in which: • fumes to be purified are passed through a gas-solid separator, • the following are fed into a quench reactor at the same time: ∘ a fraction of the solid residues discharged from the separator, this fraction amounting to between 40 and 95% of the total output of the solid residues discharged from the separator, ∘ a reagent formed from alkaline earth metal oxide, the flux of which is in the range of between 0.5 and 10% of the flux of said fraction of the solid residues, and ∘ a gaseous flux, which contains between 50 and 100% by volume of steam and the output of which is such that the stoichiometric molar ratio, defined as the number of moles of water per hour of the gaseous flux divided by the number of moles of reagent per hour, lies in the range of between 2 and 50, wherein the flow time of the solids through the reactor, during which the mixture of said fraction of solid residues and said reagent is brought into contact with the gaseous flux, ranges between 1 and 30 minutes, and • the solids discharged from the reactor are recirculated to the separator by mixing them with the fumes to be purified upstream of the separator. • fumes to be purified are passed through a gas-solid separator, • the following are fed into a quench reactor at the same time: ∘ a fraction of the solid residues discharged from the separator, this fraction amounting to between 40 and 95% of the total output of the solid residues discharged from the separator, ∘ a reagent formed from alkaline earth metal oxide, the flux of which is in the range of between 0.5 and 10% of the flux of said fraction of the solid residues, and ∘ a gaseous flux, which contains between 50 and 100% by volume of steam and the output of which is such that the stoichiometric molar ratio, defined as the number of moles of water per hour of the gaseous flux divided by the number of moles of reagent per hour, lies in the range of between 2 and 50, wherein the flow time of the solids through the reactor, during which the mixture of said fraction of solid residues and said reagent is brought into contact with the gaseous flux, ranges between 1 and 30 minutes, and ∘ a fraction of the solid residues discharged from the separator, this fraction amounting to between 40 and 95% of the total output of the solid residues discharged from the separator, ∘ a reagent formed from alkaline earth metal oxide, the flux of which is in the range of between 0.5 and 10% of the flux of said fraction of the solid residues, and ∘ a gaseous flux, which contains between 50 and 100% by volume of steam and the output of which is such that the stoichiometric molar ratio, defined as the number of moles of water per hour of the gaseous flux divided by the number of moles of reagent per hour, lies in the range of between 2 and 50, wherein the flow time of the solids through the reactor, during which the mixture of said fraction of solid residues and said reagent is brought into contact with the gaseous flux, ranges between 1 and 30 minutes, and • the solids discharged from the reactor are recirculated to the separator by mixing them with the fumes to be purified upstream of the separator.