A bull barrel is heavy, but if you are shooting targets off a rest,or trying to hit bunnies at range off a bi-pod, then it is probably fine. If you're going to be carrying it for any distance, or trying to shoot it offhand, then it probably isn't the best choice. It all depends on what you want the rifle for.
Horses for courses and all that.
If you wanted to drop the weight, maybe get in touch with someone like Scott Trail and see if he could turn it down for you. Might be an awful lot cheaper than a new barrel.
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