A CMP composition containing 5-aminotetrazole, e.g., in combination with oxidizing agent, chelating agent, abrasive and solvent. Such CMP composition advantageously is devoid of BTA, and is useful for polishing surfaces of copper elements on semiconductor substrates, without the occurrence of dishing or other adverse planarization deficiencies in the polished copper, even in the presence of substantial levels of copper ions, e.g., Cu.sup.2+, in the bulk CMP composition at the copper/CMP composition interface during CMP processing.