Combustion residue can be partially melted and/or sintered in the combustion bed of a grate furnace system. By returning the unmelted and/or unsintered combustion residue, completely sintered inert granulates are obtained. To control the melting and/or sintering processes, at least one of the following process steps is implemented: the residues are returned only as long as, and only in such an amount that the changes thus caused in the essential combustion parameters remain within previously defined tolerance limits; the combustion conditions of the combustion process are changed in such a way as to counteract the changes in the combustion parameters produced by the return; the material composition of the combustion residue is changed by the return of selected fractions of the combustion residue so that the melting and/or sintering process of the combustion residue is influenced; and the material composition of the combustion residue is changed by the addition of additives is that the melting and/or sintering process of the combustion residue is influenced.