Conventional adaptive cancellation systems using traditional transverse finite impulse response (FIR) filters, together with least mean square (LMS) adaptive algorithms, well known in active noise control, are slow to adapt to primary source changes. This makes them inappropriate for cancelling rapidly changing noise, including unpredictable noise such as speech and music. Secondly, the cancelling structures require considerable computational processing effort to adapt to primary source and plant changes, particularly for multi-channel systems. This paper describes methods to increase the adaptive speed to primary source changes in large enclosed spaces and outdoor environments. A method is described that increases the response to time varying periodic noise using traditional transverse FIR filters. Here a multi-passband filter, with individual variable adaptive step sizes for each passband is automatically adjusted according to the signal level in each band. This creates a similar adaptive response for all frequencies within the total pass-band, irrespective of amplitude, minimizing the signal distortion and increasing the combined adaptive speed. Unfortunately, there is a limit to the adaptive speed using the above method as classical transverse FIR filters have a finite adaptive speed given by the stability band zero bandwidth. For rapidly changing periodic noise and unpredictable non-stationary noise, a rapid to instantaneous response is required. In this case the on-line adaptive FIR filters are dispensed with and replaced by a time domain solution that gives virtually instantaneous cancellation response (infinite adaptive speed) to primary source changes, and is computationally efficient.