How to even out a pair of bookcases on an uneven floor

self-assembly-furniture

So, I have a couple Ikea Billy bookcases, normal. I got them with doors, so with the forward weighting, I'm a bit extra paranoid about tipping.

I put them together; all fine. Then I try to place them against the wall. I find the floor is uneven. Not just slanted, but a little bowed as well. I want them flush together, but it seems if I try to get that they don't fit together right, and are not aligned vertically. I can get them to sit nice together, but then they have a slightly forward lean (I can and will anchor to my wall with a bracket at the top).

So, if I shim enough to be perfectly level, they won't stand together right and I get a little stair step effect across the top. I also get a bad gap with the kickpanel/toepanel underneath. If I have them standing together right, they're not level across the top. Is having them level all that necessary, especially since I will be anchoring to the wall? Is there something I can do to make the gaps from shimming less noticeable? Does joining them together with bolts make sense? I saw some parts from Home Depot that can bolt them together, would that help, or would the stresses from the bookcase shear the bolts? (unlikely, but as I said paranoid about tipping).

Thanks much.

EDIT: I accepted the answer closest to what I did. But this is what I did. I realized a few things. 1) the hinges on the Billy (standard Ikea hinges) don't have to be super level to work, they have a bit of a snap action to them. 2) I'm bolting to the wall, so with this and above, I don't need to be super paranoid about level, i can just join together at sorta level.

I actually got some binding posts and some breakable/adjustable length bolts. I drilled through the shelf holes in the bookcase, trying to use the ones where the hinges were anyway. This got them together. Then I did some mild shimming, and bolted to the wall. NOTE I got 3, I probably should have gotten more. I sheared one bolt by tightening too hard. If you break before Ikea does, you're not heavy duty use. Seems to work well, and very solid.

Best Answer

Attaching the bottom of both bookcases to a single flat board will get them aligned right. Then you'll just have to shim once to get things properly vertical. If the problem is extreme, consider bolts or a backboard to connect the sides of the units. Both these options will improve overall stability of the pair. Depending on the aesthetic situation, you could use anything from 3/4" BB grade plywood to birdseye maple for the boards.