Problems smoothing out a Les Paul Guitar

Hi everyone, I’ve just started using Blender the past couple of days. Even though it’s overwhelming at times, the learning process is smooth sailing. However, I’m stuck on a problem now. I’m trying to model a Les Paul guitar; I’ve got the body shape done, but when I try to apply subsurfing to smooth it out, the bottom half looks wacky. Here’s what I mean:

That’s the body without subsurfing.

That’s the body with subsurfing (the render level is 4).

That’s the body’s polygons, thought it might help with diagnosing the problem.

If you’re using subsurf, get rid of the triangles, even sized quads behave so much better. To control the subsurf effect there are a number of ways you could look at.
Select the edge in edit mode and in the Transform Properties panel select a crease value
Add and edge-split modifier and make sure it’s above the subsurf modifier.
Add loops of vertices around the edge of the guitar.
A subsurf level of 4 is probably too high, it’ll slow down the rendering for little benefit. Use Set Smooth in the Links & Materials panel in combination with subsurf.