An improved method, system, and a computer program storage device (e.g., including software embodied on a magnetic, electrical, optical, or other storage device) for management of compressed main memory allocation and utilization which can avoid system abends or inefficient operation that would otherwise result. One feature reduces (and ultimately eliminates) all unessential processing as the amount of available storage decreases to a point low enough to threaten a system abend. In another example, the amount of current memory usage is determined as well as one or more of: an estimate of an amount of allocated but unused memory; a determination of the amount of memory required for outstanding I/O requests. The compressed memory is managed as a function of the current memory usage and one or more of the other measured or estimated quantities. The compressed memory can be managed by maintaining a set of dynamic thresholds; estimating the amount of storage that can easily be freed (used but available) and the amount of storage that is committed (allocated but unused). The estimate of committed storage can include: the current storage utilization; and an estimate of storage committed to new pages (based on the number of new pages granted), the times at which this was done, the estimated compression ratio, and estimates of residency times in the cache.