Power consumption in a non-volatile storage device is reduced by providing reduced read pass voltages on unselected word lines during a read operation. A programming status of one or more unselected word lines which are after a selected word line on which storage elements are being read is checked to determine whether the unselected word lines contain programmed storage elements. When an unprogrammed word line is identified, reduced read pass voltages are provided on that word line and other word lines which are after that word line in a programming order. The programming status can be determined by a flag stored in the word line, for instance, or by reading the word line at the lowest read state. The unselected word lines which are checked can be predetermined in a set of word lines, or determined adaptively based on a position of the selected word line.