For my example I'll use the two bevels (30°, 40°) that Spyderco's Sharpmaker uses since they claim their angles are best for most uses. Rough sharpen a knife at ~15° each side for the primary bevel. Once the knife has a utility edge, start a secondary bevel at ~20° each side using a finer stone(s) to refine and further sharpen the edge. Now comes the convexing. Place a piece of sandpaper (I prefer wet/dry) on a firm/flexible base such as a computer mouse pad and strop (edge trailing) the secondary bevel (at 20°) with light pressure. The mouse pad will give somewhat causing the sandpaper to wrap around the blade thus creating a convex curve. CAUTION: Excessive pressure will round over the edge too much. Finish with a grit that suits the knife's purpose. Using a progression of sandpaper grits will speed and refine the process. Something like 100, 300, 800, 1200 grits will produce a very sharp edge, possibly too refined for general kitchen use. (Someone may come along and tell you about "Scary Sharp" using grits of 20,000+) Some will advise you to skip the secondary bevel and convex the entire primary bevel possibly resulting in a sharper (and possibly less sturdy) edge. Your choice.
This convex edge is sturdy for general kitchen use and can be easily maintained with regular stropping. I prefer using a hanging strop (not one mounted on a hard surface) because it gives enough to easily follow the convex bevel (be careful not to round over the edge) and it works well for long kitchen knives. OR Strop on a piece of leather on top of the mouse pad. This will give your Henckels a sturdy, sharp and useful edge easily maintained with a strop. Try it on a chopping blade (chef's knife) first to see if your Henckels take on a new life. But alas, all this work will be short lived on a hard cutting board (even hard plastic).
Hopefully someone will come along and point you toward previous posts or websites that have graphics to illustrate and better specify the convexing process.
