In a radio including analog and digital portions, with at least one A/D Convener between the analog and digital portions, and the selectivity of the radio at least partly implemented in the digital domain, an AGC controller sets a first variable gain amplifier (VGA) (302) to low gain upon a determination that a wide-band power estimation exceeds a wide-band threshold. The wide-b and threshold is selected to reduce the occurrence of A/D converter saturation. If the wide-band power estimation is less than the wide-band threshold, then for each VGA (302) in the analog portion, a determination is made whether a narrow band power estimate exceeds a narrow-band threshold, corresponding to that VGA (302), plus a hysteresis value, in which case that VGA (302) is set to low gain; or whether the narrow-band energy estimate is less than the narrow-band threshold minus a hysteresis value, in which case that VGA (302) is set to high gain.