Walls and Ceilings - Remove joists on small addition?

Hi, I was wondering if anyone can give their thoughts on this question?

I have a small exterior sun porch that was tacked onto the original structure in the 60's. It's about 10ft long by 16ft wide. For the roof section, whoever built it basically tacked a small section of roof right on top of the real roof. The whole porch itself is sort of tacked on, not really integrated structurally with the rest of the house.

I was wondering with the room being so small and separate from the main structure, with the supporting end walls only 16ft apart, and the roof section being so small, could the joists be removed to have a higher ceiling with drywall on the rafters?

I realize a structural engineer probably needs to be consulted, but thought i would see what you guys thought first

Here's a link with a pic to help visualize:
Link to image of roof structure (http://jessemullis.fotopic.net/p58154367.html)

I would not remove the ceiling joists, it will sag. The rafter slope is about 3/12 (3" high per 12" horizontal), which is very shallow. A lot of pressure is at work, any modifications would not be good. Be safe, G

thank you!!! really appreciate the advice/thoughts