An annular combustor includes an inner liner shell and an outer liner shell defining an interior volume through which combustion gases flow in a gas flow direction from a forward end to an aft end. A cooling shroud is attached radially outward of the inner liner shell, forming a cooling passage between the inner liner shell and the cooling shroud. The cooling passage directs air in an air flow direction opposite to the gas flow direction. The cooling shroud is assembled from circumferentially adjoined cooling shroud segments, and the distance between the cooling shroud segments and the inner liner shell is greater at the forward end than at the aft end. Fastening elements are distributed across an axial length of the cooling shroud segments in circumferentially staggered rows. Each forwardmost fastening element is disposed immediately adjacent to a curved portion at the forward end of each respective cooling shroud segment to reduce vibration.