One of the first things folks ask, when they see one of my small carvings is: "how do you keep from cutting yourself, when you carve that small"? Well, here's one of the answers. I always leave a "Handle" on the piece of wood. This, at least. keeps the knife blade farther away from my fingers.
There is also something else that I do when I leave a "Handle" on the wood. After whittlin/carving on one end, I flip the piece of wood and carve/whittle on the other end.
Rather than "waste" wood, I'll even carve/whittle somethin in the middle of both ends. This is how I usually have a small basket full of things to give to the kids.
Another tip along these lines is that I always carry a very small dovetail/backsaw in my kit. I'll use this to cut the carvings off the stick.