A helicopter's anti-torque system is a significant contributor to radiated noise. The Fenestron, used on Airbus Helicopters, allows to mitigate the anti-torque noise by masking effect and modulation of the blade distribution. However, unlike aircraft engine nacelles, it does not contain acoustic liners inside the duct to absorb the noise radiated by the rotor blades. This paper describes: first, the FEM modelization of the noise radiation for a 1/3-scale fenestron mock-up at the 1st BPFs, in static conditions; second, the assessment of the effect of an absorbing treatment introduced inside the collector or the diffuser and defined by its acoustic specific impedance; third, the design optimization applied to different acoustic liner types, adapted to the diffuser of the mock-up. Because of the limited duct length, forward and afterward radiations interact, generating interference pressure patterns. Several types of liners (conventional and unconventional), designed to deliver a high absorption, appear adapted to dimensional constraints: SDOF or DDOF type, with a perforated plate above cavities or based on the concept LEONAR ("Long Elastic Open Neck Acoustic Resonator"). Another paper completes the study with (aero-)acoustic tests, applied to elementary samples to validate the impedance target, and performed in an anechoic room with the mock-up.