An incremental collector that employs remembered sets to identify the locations where a mutator has modified references to objects in respective heap regions employs a thread operating concurrently with the mutator to update the remembered sets in accordance with reference mutation. Specifically, when the mutator modifies a reference in one of a plurality of "cards" into which the collector treats the heap as divided, the concurrent thread ordinarily searches the card for references in accordance with which it updates the remembered set. But it selects certain cards, in which it has observed particularly high mutation activity, as ones in which reference mutation will not cause concurrent remembered-set updating. Remembered-set updating in response to those cards' references occurs only when all mutator threads have been suspended.