I have/had three Centerpoint scopes. One dropped a lens inside the tube, having it on a cf rifle probably didn't help, iirc it was the 3-7X model. I have two of the 4-16X with AO models. One lives on a Marlin 60 the other gets moved around doing load testing. One was purchased at Walmart the other came from a pawn shop ($15).
They are decent scopes for the money. They come with mounts and lighted reticles, the AO function works fine and is handy for rimfire shooting. The glass is ok, but not a match for scopes at say $150 or so, the focus is ok except at the very edge. If you switch from this scope to a more expensive one you are likely to notice a distinct difference in brightness. Eye relief is adequate, I have other scopes in this price range, the Centerpoint is the best of the bunch. Mine hold zero, no problem, the turrets work pretty well for a scope costing $70, settings are repeatable and I have no complaints about the accuracy I can achieve.
I bought a Luepold fixed 4X at a pawn shop for ~$125, sent it to Luepold and they did an overhaul on it for free. Because it has better optics and is smaller than the Centerpoints something like this might make a better small game scope. Weaver offers a nice fixed 4X rimfire scope also.
The Centerpoint might be a little big for a carrying around rifle? This my Marlin 60 with the Centerpoint 4-16AO ...
Centerpoint is supposed to have a good guarantee, but be sure to save the sales receipt, I was unable to send mine to them because I discarded my paper work. Unlike Luepold whose guarantee is unconditional (except for abuse).