Clean combustion and equilibration equipment and methods are provided to progressively deliver, combust and equilibrate mixtures of fuel, oxidant and aqueous diluent in a plurality of combustion regions and in one or more equilibration regions to further progress oxidation of products of incomplete combustion, in a manner that sustains combustion while controlling temperatures and residence times sufficiently to reduce CO and NOx emissions to below 25 ppmvd, and preferably to below 3 ppmvd at 15% O2.