A set of non-volatile storage elements undergoes initial programming, after which a reprogramming, with higher verify levels, is performed in non-real time, such as when a control enters a standby mode, when no other read or write tasks are pending. The reprogramming can program pages in the set one at a time, stopping at a page boundary when another read or write task is pending, and restarting when the control become available again. Status flags can be provided to identify whether a page and/or the set has completed the reprogramming. In another aspect, a higher pass voltage is applied to unselected word lines during the reprogramming. In another aspect, an error count is determined using a default set of read voltages, and an alternative set of read voltages is selected if the count exceeds a threshold.