An adaptive, feed-forward, ambient noise-reduction system includes a reference microphone for generating first electrical signals representing incoming ambient noise, and a connection path including a circuit for inverting these signals and applying them to a loudspeaker directed into the ear of a user. The system also includes an error microphone for generating second electrical signals representative of sound (including that generated by the loudspeaker in response to the inverted first electrical signals) approaching the user's ear. An adaptive electronic filter is provided in the connection path, together with a controller for automatically adjusting one or more characteristics of the filter in response to the first and second electrical signals. The system is configured to constrain the operation of the adaptive filter such that it always conforms to one of a predetermined family of filter responses, thereby restricting the filter to operation within a predetermined and limited set of amplitude and phase characteristics.