A number of complimentary techniques for the read scrub process using adaptive counter management are presented. In one set of techniques, in addition to maintaining a cumulative read counter for a block, a boundary word line counter can also be maintained to track the number of reads to most recently written word line or word lines of a partially written block. Another set of techniques used read count threshold values that vary with the number of program/erase cycles that a block has undergone. Further techniques involve setting the read count threshold for a closed (fully written) block based upon the number reads it experienced prior to being closed. These techniques can also be applied at a sub-block, zone level.