The invention provides a polishing composition and a method of chemically-mechanically polishing a substrate comprising a noble metal, the polishing composition comprising (a) an oxidizing agent that oxidizes a noble metal, (b) an anion selected from the group consisting of sulfate, borate, nitrate, and phosphate, and (c) a liquid carrier. The invention further provides a polishing composition and a method of chemically-mechanically polishing a substrate comprising ruthenium, the polishing composition comprising (a) an oxidizing agent that oxidizes ruthenium above the +4 oxidation state, (b) a polishing additive selected from the group consisting of metal sequestering polymers, metal chelators, organic thiols, compounds that reduce ruthenium tetraoxide, lactones, and .alpha.-hydroxycarbonyl compounds.