Where to find framing contractors who aren't general contractors

[Anthony M.]

I'm looking to act as my own general contractor for a couple rehab projects, both of which involve adding a 2nd level to a 1-level home. I'm having a hard time finding contractors who can handle the framing portion of the project (flooring joists, laying subfloor, walls, roofing system) who aren't also general contractors. It seems every company I talk to is a general contractor. 

Can anyone offer advice for how to find contractors who aren't general contractors? I don't want to pay the general contractor's premium.