After having three rifles built for me, I have to say that I'm very happy with them.
You can get somebody like Pac-Nor to put your choice of a barrel on your action and they shoot really well. Far better than I really need. I did that with my first two.
But to do it really well, you need to find a guy that has alot of experience in building the type of rifle you really want and need. I used such a person to modify my first two and to build my 3rd.
For example, I'm not interested in the last word in accuracy. While it's lots of fun shooting groups under .5 MOA with a light sporter, I'd much rather have a rifle that goes bang under the worst of conditions and a scope that will hold it's zero under such conditions. The two are not at all the same sort of rifle build, trust me.
To my mind, a custom, or customized rifle is one that better suits your needs than one that I can buy off of the rack. Just what those needs and desires are, are up to you and your pocket book.
Beware of doing this however. I was convinced that only one would do. Now I have three and I've customized a couple of others quite a bit. It's is an aquired, very expensive addiction. E
