I'm familiar with the basics of good bellows technique. I mentioned half-pumps just to describe the behavior of my current bellows. What I meant is that from fully closed to half open, my current bellows draws in almost no air. That phase of the pumping cycle just pulls the gusset from the ballooned position to the sucked-in position, without much change in the volume of air in the bellows.
I imagine my bellows, a better SSP bellows, and an accordion-style musette bellows (all of equal clapper area) performing like this:

Because the gusset on my bellows billows in and out, there is a plateau just after fully open and fully closed. During that phase, the movement of my arm is not moving any air (or not much). This is problematic for air control. For a better SSP bellows, I would imagine this effect to be reduced. For an accordion-like bellows, I would imagine the maximum volume to be lower than the others, but I would expect the function to be linear because there should be almost no billowing of the gusset. An accordion-style bellows should approximate a piston, except that the volume can't go to zero. There will be some residual volume because the stack of wire ribs would prevent complete clapper closure. I would expect this to prevent too much of a poorly controlled "huff" at the volume minimum, when the elbow is all the way down. From an air control standpoint, this seems ideal. Slightly larger clappers could compensate for the smaller volume. A three-clapper bellows would fall somewhere between the blue and green lines, I would imagine.
Is this reasoning consistent with your experience, CHasR? I think, since you mentioned that the accordion-like bellows suck, that one or more of my guesses must be off. Maybe that little bit of curvature in the blue line helps to stabilize bag pressure?