A technique for managing data storage includes generating entropy of blocks on a per-block basis and selectively performing inline compression on blocks based at least in part on their entropy. Entropy of a block provides a rough measure of the block's compressibility. Thus, using per-block entropy enables a storage system to steer compression decisions, e.g., whether to compress and/or how much to compress, flexibly and with high granularity, striking a balance between throughput and storage efficiency.