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Primer strike off center ??

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My new to me lightweight Officer model is striking the primers off center. The barrel does have a little up and down play when I press down on it through the port on the slide. But the gun shoots exactly where you point it. It has been worked on by someone in the past, chamber opened up for feeding, new sights and God only knows what else. But is this something I should be concerned about? Like I said, it shoots to point of aim, each and every time.