I have a fixed pier in an observatory building. The mount has just come back from a tune-up at Darkframe Ltd, so I needed to realign it.
The only thing I would say to my fellow users is: when you re-tighten your alt & az axes, you will worsen the alignment. It may be an idea to re-tighten these axes gradually, correcting the alignment as you go.
By the time the night was over, I had 21 stars in my sky model in CPWI, and managed to expose three hours on Makarian's chain before fog stopped play. I had not expected to achieve anything more than realignment and rebuilding my sky model, so I was a happy bunny.
From the use of CPWI I assume you are using a Celestron mount... It sounds as thought he alt/az adjustments are just as bad as those in the Skywatcher EQ6, which also throws itself out of alignment as you tighten up. That's one of the reasons that I will not introduce a polar alignment routine that requires Alt and Az to be aligned separately - tightening one can easily throw the other off 