A garbage collector that employs the train algorithm to manage a generation in a computer system's dynamically allocated heap maintains for each of the generation's cars a respective remembered set that identifies all locations where references to objects in that car have been found by scanning locations identified by the mutator as having been modified. To avoid some of the expense of remembered-set updating, the collector refrains from attempting to add to a remembered set any reference located in a car that will be collected during the next collection increment. Additionally, if no mutator operation will occur before a collection set of one or more cars will be collected, any reference located outside that collection set but referring to an object within the collection set is not recorded in a remembered set but is recorded instead in a scratch-pad list of entries that identify references to collection-set objects that need to be evacuated.