I have a problem with light in my kitchen.

I want to put in some recessed lights but have limited clearance.

Above the kitchen is a bathroom with a poured concrete floor. This
leaves me 5" of clearance from the subfloor (planks supporting the
concrete) to the bottom of the joists.

I have found IC recessed lights as shallow as 5 1/4" but that's as close
as I can get. There are non-IC lights that fit in the space but with
only 1" of clearance above (which makes me nervous).

The ceiling is out so I have full access at the moment.

Ideas?

Thanks,
*moc