I have a BLR short action takedown with fiber optic sights.
It has weaver 2 peice bases, Leupold PRW low rings, and a 40 mm scope. Lots of room for the sights.
However, the takedown option doesn't work right now, because the rear sight will hit the scope bell if I slide the barrel out of the action.
To remedy this, I am going to switch to the Leupold QRW rings on the weaver bases. The QRW are basically the same as the PRW, except they have a quick release wingnut.
I might also remove the sights, I haven't decided yet.