We present a general technique for garbage collecting old versions for multiversion concurrency control that simultaneously achieves good time and space complexity. Our technique takes only $O(1)$ time on average to reclaim each version and maintains only a constant factor more versions than needed (plus an additive term). It is designed for multiversion schemes using version lists, which are the most common. Our approach uses two components that are of independent interest. First, we define a novel range-tracking data structure which stores a set of old versions and efficiently finds those that are no longer needed. We provide a wait-free implementation in which all operations take amortized constant time. Second, we represent version lists using a new lock-free doubly-linked list algorithm that supports efficient (amortized constant time) removals given a pointer to any node in the list. These two components naturally fit together to solve the multiversion garbage collection problem--the range-tracker identifies which versions to remove and our list algorithm can then be used to remove them from their version lists. We apply our garbage collection technique to generate end-to-end time and space bounds for the multiversioning system of Wei et al. (PPoPP 2021).