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If they are tomonagura, you should get an acceptable edge from them. The fact that the edge is not better as the water becomes clear is strange.

Everyone has their own methods, but to see what a...

I don't know anything about that nagura, but my advice is this on a stone where you're getting marginal performance:
* shave with your marginal edge
* 10 very light passes, slow, be sure to get the...