The bottom of a clay bowl can be a surprisingly effective sharpener and it’s quick and cost-free also. Alternate on different bowls and they won’t concave. The only problem is you have to wash the bowl afterwards. I was a big fan for years. Then while surfing on this kitchen blog HealthyKitchen101 the other day, I came across a review of a hand-held sharpener where they mention that one of the sharpening slots is made of ceramic and has the same effect as the bowl bottom. I’ve got one and have been happy ever since