In this video Yuri Marmerstein presented a great way to further increase the strength and balance for a handstand.
It may not look like it, but Yuri is actually trying to get out of balance on purpose. As he tests the limits by leaning forward and backward, Yuri is developing and isolating different reactions to stay in a balanced position. He says that after you manage to isolate those reactions and develop reflexes, you are ready to try and take your balance out of the center as much as you can without falling down, but bringing yourself back to the handstand position instead.
The goal of this workout is to gain better control over every movement in the handstand and strengthen your core. I first came across this drill in The True Art and Science of Hand Balancing by Professor Paulinetti and Bob Jones. Its great for the control necessary to do advanced stunts, or just stand in a handstand for a long time (because you need these skills to save the balance.)