When I “finished” the project two months ago, I noticed that the panel face was very slightly concave. Here, I’ve placed a 36” long straight edge on the panel. The panel dips about 1/16” in the center.

 

That’s not very significant, but the gap on the wall side might be noticeable if the wall is slightly convex. As the time to deliver and install the shelf grew near, I decided to make a quick attempt to flatten the panel. I made an L-shaped brace from a scrap of pecan (the hardest wood I had) and screwed it into place. 

 

I didn’t measure the gap before and after adding the brace, but it didn’t seem to make much of a difference. I thought about adding glue between the side of the brace and the panel (I could clamp the panel and brace to my workbench to force flatness while the glue dried), but I decided to leave things as-is. The brace didn’t yield the results I wanted, but it adds little weight and reinforces the panel, so I left it in place.