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All the videos that I've watched on dilucot honing use something in the neighborhood of 20 strokes on each side of the bevel before diluting with a single drop of water. You may have to do something...

If your coticule is improving the edge as slowly as you seem to be describing, then you may have a really slow stone. You might try a little more slurry and not diluting as fast.

If it was just pulling, try this. Do 40 slow x strokes on your coticule with a thin coating of clear water. Watch the water and make sure you're pushing it evenly across the whole blade; re-wet if it...

It's nice when you get the first one under your belt. I've recently accomplished the same feat, and shaving with your own edge is a real thrill.