The invention is directed to a method of polishing a silicon-containing dielectric layer involving the use of a chemical-mechanical polishing system comprising (a) an inorganic abrasive, (b) a polishing additive, and (c) a liquid carrier, wherein the polishing composition has a pH of about 4 to about 6. The polishing additive comprises a functional group having a pKa of about 4 to about 9 and is selected from the group consisting of arylamines, aminoalcohols, aliphatic amines, heterocyclic amines, hydroxamic acids, aminocarboxylic acids, cyclic monocarboxylic acids, unsaturated monocarboxylic acids, substituted phenols, sulfonamides, thiols, salts thereof, and combinations thereof. The invention is further directed to the chemical-mechanical polishing system, wherein the inorganic abrasive is ceria.