I put together a new setup and I've discovered that I'm out of UP elevation adjustment before I even made it to 100 yards.

What do I need to do to get more adjustment?

Current setup is a Savage 16 chambered in 204 Ruger (32grain midsouth bullet) topped with a Browning 5-15x40 scope with LOW Leupold Rifleman Vertical rings.

I totally forgot about Burris Signature Rings. I think it's time for a trip to town to buy some rings and insert.

You could try tapered bases.

If you are out of up adjustment it may be because you have corrected too much windage adjustment on the 'scope itself rather than centering it and setting the windage adjustment on the mounts.

I did this with a Pecar. Once the mounts were set right - Redfield type - then I could take off all the windage I'd put on the 'scope using the adjustment knobs.