While working on my gooseneck cabinet last night, I noticed that there was a slight hump in the middle pine shelf board. This is to be expected, given that the stock is prepared by hand and will almost never be perfect. In most cases, it would be totally fine to leave it. This case, however, is not a standard case. This case is a case that will hold prized possessions, perhaps some rare books, or other delicate items. Anything other than a flat, smooth shelf surface will potentially cause damage to those items and it must be fixed.
I wanted to wait to remove this hump until the case was glued up so that I could ensure that the pine (which is made of a 2" wide cherry facing strip and a 9" wide white pine filler) would line up with the cherry perfectly. I glued up the shelf boards in situ after the case was assembled. To remove this hump, I turned to a trusted friend, a paring chisel.
No, I don't mean a chisel with a stubby blade and a long handle (these are not true paring chisels no matter what the ad men say). I mean a proper parer, one with a long, thin blade that makes Kate Moss look positively Reubenesque. One that is preferably made of a proper vintage steel that takes a ridiculously low bevel angle and is sharp enough to split atoms. My favorite chisel (the one I used last night) is an 5/8" wide, 3/16" thick, 8" long vintage Ibbotson with a boxwood handle. It has a sub-20 degree bevel on it... yes I have to sharpen it very often but it works so very well that I don't mind.
To make use of the chisel, I referenced the blade on the cherry front strip. Pushing the blade down into the surface, I raised the back end of the handle slightly. This flexed the chisel a tiny amount. I then slid the chisel forward carefully at an oblique angle to the grain of the wood, paring halfway between with the grain and directly across it.
The chisel references the front strip, keeping the paring chisel from cutting too deep into the shelf board. Once you've hit an area that needs to be removed, simply flex the chisel a bit by modulating the pressure used to flex the chisel. This will move the chisel forward slightly, allowing you to remove fine whisper-thin shavings. You can also simply push the chisel into the work with the handle, but you lose control so quickly that I do not recommend this technique, especially given the necessary proximity of your off-hand. I have no doubt that my Ibbotson could just about take a finger off if it were stuck into the "right" spot.
Repeat the process until you've achieved a smooth surface. Any remaining fibers can be scraped away or simply hit with 220 sandpaper. I hope this helps you to think beyond planes when faced with a tight space.