The invention provides a chemical-mechanical polishing composition comprising (a) abrasive particles, (b) a cobalt accelerator selected from a compound having the formula: NR1R2R3 wherein R1, R2, and R3 are independently selected from hydrogen, carboxyalkyl, substituted carboxyalkyl, hydroxyalkyl, substituted hydroxyalkyl and aminocarbonylalkyl, wherein none or one of R1, R2, and R3 are hydrogen; dicarboxyheterocycles; heterocyclylalkyl-α-amino acids; N-(amidoalkyl)amino acids; unsubstituted heterocycles; alkyl-substituted heterocycles; substituted-alkyl-substituted heterocycles; N-aminoalkyl-α-amino acids; and combinations thereof, (c) a cobalt corrosion inhibitor, (d) an oxidizing agent that oxidizes a metal, and (e) water, wherein the polishing composition has a pH of about 3 to about 8.5. The invention further provides a method of chemically-mechanically polishing a substrate with the inventive chemical-mechanical polishing composition. Typically, the substrate contains cobalt.