under vs underneath

Either is OK.

"Underneath" to me implies it is hidden in some way but that could just be local usage.

I get the same impliction.

um, well, USUALLY they're interchangeable, probgably at least if you're talking physical objects--and it's probably true that "underneath" has somewhat the connotation that what's under is smaller and completely overwhelmed by what's above it, like "I'm underneath an elephant". If it's not a physical object, I'm not sure they're interchangeable. Something can be "under consideration", i.e. you're thinking about it. You probably wouldn't use "underneath consideration". If you did, it would probably be perceived as similar to "beneath consideration", i.e. not even worth thinking about. Something can be "under construction", i.e. it's being constructed. It can't bde "underneath construction". (Well, you might be talking about the untouched basement of a building which was being rehabbed above ground, but that's really stretching it).

Other times you might use only one of the two:

"I'm under her" (she's my boss)
"I'm underneath her" (she's sitting on top of me)(you might also say this if she's beinng particularly bossy and you're really feeling put upon)
"I'm feeling under the weather" (I feel sick)(idiom; idioms generally require a set form of words)