This might be a rather a dumb question. I tried doing a search but get too many possibilities, and it would take forever to scroll through them looking for an answer to my question.

I would like to have an undermount sink but would love to have it flush with the counter. I don't believe I've seen this and I'll bet there's a reason for that. As it is, sinks are so deep and with my back problems and short-ish arms I would like to be able to shorten it up any way I can without giving up the swish-the-counter-water-and-crumbs-into-the-sink advantage of an undermount. I hope to have soapstone counters--yes, very heavy.