An earpiece of an ANR device incorporates one or more of feedforward-based ANR; feedback-based ANR; passive noise reduction (PNR) of environmental noise sounds in the environment external to the casing of the earpiece in higher audible frequencies; a controlled leak acoustically coupling the front cavity to the environment external to the casing of the ANR device where the coupling may be through another cavity that is closable to the environment external to the casing with a leaky cover; a combination of an acoustically resistive port and a mass port coupling a rear cavity to the environment external to the casing where the coupling may be through another cavity that is closable to the environment external to the casing with a leaky cover; a feedforward microphone given acoustic access to the environment external to the casing through an aperture that is overlain with a leaky cover or that is enclosed within a cavity that is acoustically coupled to the environment external to the casing with a leak.