How can I make the bending smoother on my rigged arm? I'm creating a minecraft rig, and I'm a bit unique, and want some smoother bends on the arm as shown:

Now, I'm not fond of the look of the inner part of the bend. I'd like to make the curve look better, so it's closer to the red line as shown. What ways can I accomplish this?
If not possible, I'd like it to be a sharp bend on the inner part. I'd highly prefer the smoother bend on the arm though.
Why not add an additional bone from the middle of the vertical bone, with a "StretchTo" bone constraint tied  to the midpoint of the next bone. Then you can assign the vertices on the inner part of the elbow to the new bone. As the elbow bends, the bone (and the vertices bound to it) should deflect like you are asking.