A method for improving a slag quality of slag in a grate firing system. The method includes providing slag in a grate firing system including a combustion chamber disposed above a combustion bed. The combustion bed has a plurality of fixed-bed burnout zones in series on a combustion grate. The fixed-bed burnout zones include a first series of fixed-bed burnout zones and a second fixed bed burn-out zone disposed downstream of the first series. The first series of fixed-bed burnout zones is traversed with a flow of oxygen-containing gas. A portion of the combustion bed associated with the second fixed bed burn-out zone is traversed with a flow of a hot combustion gas from the combustion chamber.