I have had many knives that I have sharpened with a similar method as to what Mextreme is talking about but these usually started life with a single, secondary bevel. I have routinely sharpened my Benchmades via a Lansky system by first knocking the bevel down with the 17 degree setting, then again at 20 degrees. I then sharpen the final edge with the Sharpmaker and use it for touch-ups. This tri-bevel edge serves the same general purpose as a convex edge and cuts much better than a single, steep bevel. It is not, however, a true convex edge. It also does not eliminate the problem with the edge becoming thicker over time. This is not a problem with a hollow ground blade as the steel remains relatively thin a long ways behind the edge. If you take 1/8" off your properly ground blade using a hollow grind, after sharpening for many years you still have a servicable blade. The same amount off a convex ground blade is going to result in a much thicker edge. This is especially true on the F1 which has a much heavier edge than what you would find on a Marble's.
BTW, I am not saying that you cannot put a true convex edge on a knife using a stone, you most certainly can. I just find it much easier to do using the paper/pad method. Another benefit of this method is that your blade keeps it's good looks much longer. When properly done it is very hard to tell that the knife has ever even been sharpened.