I tried some shots yesterday. f/16 seemed to be the beginning of me losing sharpness. And yes, Arizona - f/11 and right around there where incredibly crisp. I had read somewhere that a couple stops above the largest aperture would generally be the "sweet spot" for the lens. That seems to be fairly true in this case: f/5.6 and f/8 were very crisp, but the depth of field had suffered a bit for general landscapes... but it was still good to know.

Thanks everyone! Please pour on the advice. This is a new area of learning for me.