A combustor heat shield has lips with fins distributed on the lips. The lip-fins have an extended end portion projecting rearwardly from the back face of the heat shield. Impingement jets may be directed against the rearwardly extended end portions of the lip-fins to enhance cooling. The heat shield may define a fuel nozzle opening surrounded by a rail on the back side of the heat shield. Impingement holes or slots may be defined in the rail for allowing cooling air passing therethrough to impinge upon the lip-fins.