This article describes Memory Squeeze (MemSZ), a new approach for lossy general-purpose memory compression. MemSZ introduces a low latency, parallel design of the Squeeze (SZ) algorithm offering aggressive compression ratios, up to 16:1 in our implementation. Our compressor is placed between the memory controller and the cache hierarchy of a processor to reduce the memory traffic of applications that tolerate approximations in parts of their data. Thereby, the available off-chip bandwidth is utilized more efficiently improving system performance and energy efficiency. Two alternative multi-core variants of the MemSZ system are described. The first variant has a shared last-level cache (LLC) on the processor-die, which is modified to store both compressed and uncompressed data. The second has a 3D-stacked DRAM cache with larger cache lines that match the granularity of the compressed memory blocks and stores only uncompressed data. For applications that tolerate aggressive approximation in large fractions of their data, MemSZ reduces baseline memory traffic by up to 81%, execution time by up to 62%, and energy costs by up to 25% introducing up to 1.8% error to the application output. Compared to the current state-of-the-art lossy memory compression design, MemSZ improves the execution time, energy, and memory traffic by up to 15%, 9%, and 64%, respectively.