The invention provides a chemical-mechanical polishing composition comprising (a) abrasive particles, (b) a cobalt corrosion inhibitor, (c) a cobalt dishing control agent, wherein the cobalt dishing control agent comprises an anionic head group and a C13-C20 aliphatic tail group, (d) an oxidizing agent that oxidizes cobalt, 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.