Read disturb is reduced in non-volatile storage. In one aspect, when a read command is received from a host for reading a selected word line, a word line which is not selected for reading is randomly chosen and its storage elements are sensed to determine optimized read compare levels for reading the selected word line. Or, a refresh operation may be indicated for the entire block based on an error correction metric obtained in reading the storage elements of the chosen word line. This is useful especially when the selected word line is repeatedly selected for reading, exposing the other word lines to additional read disturb. In another aspect, when multiple data states are stored, one read compare level is obtained from sensing, e.g., from a threshold voltage distribution, and other read compare levels are derived from a formula.