Have you ever tried a bread knife with so-called "micro-serrations" (really something like ~0.5mm tooth depth / pitch)?

The one I have seems to cut just as cleanly as a chef's knife once within a material, but has better ability to bite into material at the start of a cut, when a chef's knife would be slipping off. (Think: a freshly-baked loaf of high-sugar bread, where the outside is relatively stiff, but the inside is so soft that the outside tries to "squish away" from a non-serrated slice.)

I would never use it for dicing, but it's oddly goot at e.g. slicing watermelon.