My BLR/.358 has Weaver bases and these Leupold rings holding the 1-4x20 Leupold in place. Nice and low. My BLR/.358 is a steel receiver gun and the rear sight is very close to the receiver/barrel joint. I'm not sure a 33mm scope would fit over it (rear sight) on low rings ??? If your BLR/.358 is an alloy receiver gun, the rear sight is 1.5-2" farther out the barrel and I'm pretty sure these lows would work fine then. I also have a BLR/.325 with a 2-7x33 30mm Leupold on it in medium height Warnes, it's a bit high to my taste.