The one that we have is similar, but it is a "single-layer" drawer, and our coffee maker sits on top of it. This way, it sucks-up less counter-top space, and is nice and convenient.
If you can narrow-down the types of coffee that you like, there are plastic "bins" that are available, which stack together like books. You slide them out of their space and fill from the top with k-cups. Then, via a sloped "floor" within each bin, you can grab K-cups from the bottom front of each bin. The nice thing here is that each bin holds at least a full 18-count box of K-cups.
(With most of the "carousels" and small drawer systems, you STILL need to determine where to store the partially-opened boxes of K-cups that you do not have loaded into your "handy storage".)
Hope this helps