A memory device and associated techniques for reducing hot electron injection type of disturbs of memory cells. In one approach, after a pre-charge operation, voltages of a first group of adjacent word lines comprising a selected word line (WLn) and one or more drain-side word lines of WLn are increased after voltages of remaining word lines are increased. In another approach, after the pre-charge operation, voltages of the first group of adjacent word lines are increased in steps while voltages of remaining word lines are continuously increased. In another approach, voltages of the first group of adjacent word lines are increased from a negative voltage while voltages of remaining word lines are increased from 0 V. In another aspect, the disturb countermeasures can be implemented according to the position of WLn in a multi-tier stack.