I've been stepping at a normal speed but quietly to distract people less. On 9/5/2011 I took it to a treadmill. It was nearly silent compared to the thuds I'm used to hearing with each footstep. At first I found it easiest to achieve this effect by stepping only with the balls and toes of my feet. Then I found that I could bring my foot down beginning with the ball but smoothly coming down further later in the step to achieve even greater silence. Because the energy of each step is transferred more slowly to the treadmill because I bring my foot down slowly, it is better for my bones - osteoarthritis is a much greater risk for runners.
It made my calves sore. I took this to the Biology Forum on physicsforums.com; and they told me that it sounds similar to toe running, which is commonly observed to make the calves sore until the muscles adjust.
If you imagine my foot moving in a straight line toward the ground, the change (d) in its linear momentum (p) over time (t) is the force (F) of the impact; so the longer it takes for the impact to occur, the less intense the force of the impact. Force equals mass*acceleration (ma), so the force of the impact is equal to how much the vectors of the atoms in me and the ground change due to the interaction of their electrostatic fields (and whatever else is involved in the interaction of atoms during a collision of the objects composed of such particles).
9/11/2011: I ran some more today. I realized that the trick is to land flat footed but to control the speed at which my foot is moving when it touches the ground so that it has less force at the time of impact.