Sometime and nice exercise is to rest the hand on the fingernails rather than the meat of the fingers and try to move the arm and wrist as one with the hand. If you just try to use the hand then it will amplify and unsteadiness. Try some connected uppercase Os, it is always a nice exercise.
It's just as bad on lined paper... trust me.
The problem with speed is that if I slow down, my naturally shaky hands make it even worse.