I have never heard falling step in boxing...step and slide...same thing?...though I have seen many take a step then fall...
I've trained only a little in boxing, but I've been told to punch higher than my head because my forward step reduces height. But Dempsey's insistence of eliminating the preliminary step is to reduce telwgraphing at the expense of recruiting power from the stretch reflex. As Prof Bono states, I believe Dempsey is merely using older language to describe the step-n-slide since there is really no extended sliding, only lifting the foot and, well, letting the body fall into the step with a launch from the rear foot.
Heya Gints, you are right that a lot of the use of level change and head movement has to do with not telegraphing and/or confusing the enemy. The actual power component is just basically aligning the body and getting as much of your body force going in the direction through the target.
A question, after your forward step, are you punching from the hip, such as done with a "shovel hook" or a "rising punch"?
This type of striking is more complex than the "falling step" alone. There are various ways to generate the power, IME, in boxing and one is using the "falling step" and another is using the "shoulder whirl" (power from hip and shoulder rotation). However, there can be a little falling step to add power when primarily using the shoulder whirl for power. And, conversely, when primarily using the falling step for power, you can add some shoulder whirl for added power.
In addition, the alignment of the body and pivot points used also help determine how much force goes through the target opposed to back into you or in the opposite direction.
I really like this video with GGM Gaylord to demonstrate some of the footwork:
http://www.youtube.com/watch?v=9ia-HuNTUS0 One thing I like about the strikes is that GGM is great at showing his body moving in the direction of the strike. When at 12 seconds the first back fist shows the footwork of a "falling step" with a lead left. Then it is followed by a second back fist with a bigger movement and more power. In both steps, he first shifts his weight back so the strike is more telegraphed; however, at the point where the foot strikes the ground and he actually strikes, the force is moving all forward into the target (this is the concept of the falling step to convert downward force into forward force). Later in the video, when he strikes down, the force of his body is moving down, when he strikes up, the force of his body is moving up.
The basic falling step is for a straight punch that is parallel to the ground. If the strike is going to be down or up, then the force of body would move down or up respectively. Hope I'm making sense.