Depending on how much you have to move the nock, I would recommend moving the rest up. When you move the nock you also change the distance from the nock to the peep, or kisser. This will require a change in your anchor as well to still see through the peep or line up the kisser. Move the rest if you can and if the move is small. 6 inches at 20 yards will require a fairly decent sized move though.

Second option/thought, you could be picking up some rest/fletch contact, this would kick the tail up and drive a BH arrow down.

--Bob