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Whatever optic you choose, make sure the parallax can be adjusted fairly close. Many cheaper optics have fixed parallax, and those that are adjustable will only go down to 50 yds. Not ideal when you may want to use a rimfire at 10-25yds.
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I respectfully disagree. There's nothing wrong with parallax adjustment but it should not be your priority.
I have a Leuopold VX2 3-9x33mm EFR and it's a great scope, but I prefer the optics on the VX-2 3-9x40mm and even though it's a centerfire scope with the parallax fixed at 150 yards, it's not a problem.
Focus at 10-25 yards isn't an issue at 3x-4x and parallax error is so minimal that it can be ignored for all practical purposes, unless you've got a really poor fitting stock and/or a poorly mounted scope that results in very inconsistent eye placement.
The only place where an EFR scope matters is if for some reason you need to use maximum magnification with razor sharp focus at 10-25 yards, and there just are not that many instances where you need an apparent target distance of 1.1 to 2.8 yards.
Consequently, I advise placing the emphasis on the best optics you can afford, without spending the budget on things that don't really matter - like parallax adjustment and close focus capability.