Guess what your saying is that the back/spine are feeling pressured or tense? As long as the spinal erector are even in a average, or normal condition, a compression of the disc should be no problem. But than again, always the exception. Though, if your developing a herniated (most don't realize that possibility) that may be a issue.
Just throwing this idea in, but might try hanging/stretching before working out, rather than after feeling discomfort (or even between sets). Your right in hanging from a overhead bar, allowing the body to settle in, as it were. Some with compressed disk have found relief that way. Using a dipping belt, with added weight has also given a better stretch to the spine. Hanging has also helped many men with tight shoulder muscles & joints. So use a wide grip, some closer...take your pick or use any grip version you want. ....your body.
Good Luck.
