Methods for echo estimation or echo management (echo suppression or cancellation) on an input audio signal, with at least one of adaptation of a sparse prediction filter set, modification (for example, truncation) of adapted prediction filter impulse responses, generation of a composite impulse response from adapted prediction filter impulse responses, or use of echo estimation and/or echo management resources in a manner determined at least in part by classification of the input audio signal as being (or not being) echo free. Other aspects are systems configured to perform any embodiment of any of the methods.