The LED UCL thread and follow on discussion might help.

The typical profile for direct wire lights is between 1" to 1.25". If you want lower profile lights which generate minimal heat, your most viable option is led. Lights like the eW profile are also dimmable.

The LED UCL thread and follow on discussion might help

Where is that thread?

updated to add: Maybe I found it. Is this the one you meant? led ucl continuation

This post was edited by marti8a on Wed, Oct 30, 13 at 23:37

Yes, that is the follow on

I read and re-read that continuation, and it was way more than I could absorb.
I too, have only 3/4 inch under the cabs, plus some weird corner configurations.
First, you will have to go with LED lights. But they come in cool or warm, diffused or not, pucks (uck), and can be configured any way you want, including in the corners.
Go to Environmental Lights.com and they have a section on low profile lighting. You can request a lighting plan from them; provide the details and in a day they will send back the specs for a plan with their lights. If they need more info, they'll ask. The estimate will be there.
It doesn't cost to get an estimate, and you'll have an answer to the electrician saying "they don't come that shallow"

idabean