Methods, computing systems and computer program products implement embodiments of the present invention that include identifying, in a storage system including multiple storage devices having respective sets of storage regions, respective default low storage region thresholds that are used for garbage collection. For each given storage region, a time threshold and an alternative low storage region threshold greater than the default low storage region threshold for the given storage device are defined. While processing input/output operations for each given storage device, a count of unused storage regions in the given storage device is maintained, a timer is initialized, and upon the timer matching the time threshold for the given storage device, a garbage collection operation is initiated. In some embodiments, processing the input/output operations includes using a log-structured array format.