Speech enhancers suppress impairments in an acoustic signal. An audio appliance has a first microphone and a second microphone. The first microphone provides a first signal, and the second microphone provides a second signal. A voice-activity detector can determine a presence of user speech responsive to a combination of voice-activity cues, including a first level difference between the first signal and the second signal within a first frequency band, and a second level difference between the first signal and the second signal within a second frequency band. A noise suppressor suppresses impairments originating from a direction of, e.g., up to about 75-degrees from an axis extending from the second microphone to the first microphone. An output device can output a noise-suppressed output-signal corresponding to a determined presence or absence of speech by the voice-activity detector. The impairments can be suppressed by, e.g., between about 3 dB and about 20 dB.