Combustor panels for use in gas turbine engine combustors having a panel body having a peripheral rail around a periphery of the panel body, a first boss formed on the panel body and surrounding a first aperture that passes through the panel body, and a first webbing that extends from the peripheral rail toward the first boss. A first annular channel is formed between the first webbing and the first boss and surrounds the first boss and a first web pocket is formed within the first webbing between the peripheral rail and the first boss and defines a local extension of the first annular channel extending from the first boss to the peripheral rail.