Systems, apparatuses, and methods for implementing a multi-tiered approach to cache compression are disclosed. A cache includes a cache controller, light compressor, and heavy compressor. The decision on which compressor to use for compressing cache lines is made based on certain resource availability such as cache capacity or memory bandwidth. This allows the cache to opportunistically use complex algorithms for compression while limiting the adverse effects of high decompression latency on system performance. To address the above issue, the proposed design takes advantage of the heavy compressors for effectively reducing memory bandwidth in high bandwidth memory (HBM) interfaces as long as they do not sacrifice system performance. Accordingly, the cache combines light and heavy compressors with a decision-making unit to achieve reduced off-chip memory traffic without sacrificing system performance.