A cooled acoustic liner useful in a fluid handling duct includes a resonator chamber 52 with a neck 56, a face sheet 86, and a coolant plenum 80 residing between the face sheet and the chamber. Coolant bypasses the resonator chamber, rather than flowing through it, resulting in better acoustic admittance than in liners in which coolant flows through the resonator chamber and neck. In one embodiment, the liner also includes a graze shield 88. Openings 40, 38 penetrate both the face sheet and the shield to establish a relatively low face sheet porosity and a relatively high shield porosity. The shielded embodiment of the invention helps prevent a loss of acoustic admittance due to fluid grazing past the liner. Another embodiment that is not necessarily cooled, includes the resonator chamber, low porosity face sheet and high porosity shield, but no coolant plenum for bypassing coolant around the resonator chamber. An associated method of retrofitting an acoustic treatment into a fluid handling module includes installing openings in the module and mounting a resonator box 44 on the module so that the inlets to the resonator necks register with the installed openings.