A coated cutting insert for removing material from a workpiece that includes a substrate is disclosed. A wear-resistant coating on the substrate that includes an alumina layer and a Zr- or Hf-carbonitride outer layer deposited on the alumina layer. The Zr- or Hf-carbonitride outer layer is subjected to a post-coat wet blasting treatment. The wet blasting changes the stress condition of the exposed alumina coating layer from an initial tensile stress condition to a compressive stress condition.