Search until you find a used Remington 58x. They came in 580 (single-shot) 581 (clip) and 582 (tube). It was the economy version (maple versus walnut) of the 54x deluxe match rifle. Unbelievably accurate, six-lug bolt, 60� bolt throw and 24" barrel all in a sub-five-pound rifle.
Mine is a 582 tube-fed. I had it drilled and tapped to fit better bases and have a Burris 4X rimfire (adjustable objective!) scope on it. If there is more than one ragged hole at 25 yards, it was the jerk on the trigger's fault.
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Mine is a 581-s. The plastic magazine looks cheap but works flawlessly, and as Rocky said is very accurate.
When I bought mine I didn't know about the accuracy reputation of these rifles, it was the ergonomics that got me to buy it, the gun just fits me. That, and the price was right $125 about 8 years ago, I don't know what they run now.
Boy was I surprised how it shot.