I have a circle, which I have extruded and converted to a mesh. Now the problem is that the edges run only from side to side and that doesn't give me good results when I try to deform it.  Now is there a simple way to add edges to the mesh?

CTRL+E>loopcut or hot key K  for the knife tool to cut across existing edge loops.

Start over and this time don't use a Curve circle.  Start with a Mesh circle (reduce to 16 verts) this will allow you to control how the faces and edges are made.

Quote - CTRL+E>loopcut or hot key K  for the knife tool to cut across existing edge loops.

 
Thanks for the tip. I think that was somewhere in the back of my mind, but I got the crazy idea of connecting the vertices with F. I didn't want to do that, though, because it would have been too tricky and time-consuming.

Quote - Start over and this time don't use a Curve circle.  Start with a Mesh circle (reduce to 16 verts) this will allow you to control how the faces and edges are made.

I'll try that, too.

Attached Link: Edit Mode

Okay, time for an update. I tried using a Cylinder, but that wasn't any better. I eventually went into 3ds max where I could manipulate the mesh density of the cap ends. (Sometimes, I wonder how Blender gets along without some of this stuff). And that looked okay when I imported the cylinder mesh into Blender, but it still wasn't showing the correct wireframe in Object Mode.

I don't understand what you're trying to accomplish.  You say you want to deform it, how do you mean?  Why not just add a plane..   sub surface it 4 or 5 times and then apply the modifier? 

You'll get what I got above. 

Won't that work for what you want?

 

Quote -
I don't understand what you're trying to accomplish.  You say you want to deform it, how do you mean?  Why not just add a plane..   sub surface it 4 or 5 times and then apply the modifier? 

You'll get what I got above. 

Won't that work for what you want?-

Yeah, sorry, I'm trying to take a mesh that looks a lot like that and use the Sculpt tool on it. I've tried several methods that failed, but this one looks like it could actually work. Now that I think about it, I could've probably used retopo or bump mapping. Ah, well.

Thanks a lot :)

Quote -
Yeah, sorry, I'm trying to take a mesh that looks a lot like that and use the Sculpt tool on it.

I see.  Hope that works for you.