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.

It is better to do one thing well, than to do many things and excel at nothing.