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Those Billy shelves weren't designed to stand free-floating without wall anchors - that's the core problem. Wall anchors are your quickest fix and honestly the safest route; screw it into the studs if you can, or use heavy-duty anchors if not. The dowels probably aren't the issue unless they're visibly cracked, but if you want to tighten things up while you're at it, you can replace them. Since it's from 2008 and still structurally sound, anchoring it to the wall beats buying new unless you're just tired of looking at it.

The wobble usually comes from the dowels loosening where the frame joints connect, not just the back panel failing to brace it. Before anchoring to the wall, try tightening or replacing those wooden dowels inside the side panels - they're easier to access than you'd think, and it often solves the rocking without needing to commit the shelf to a permanent spot.

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