How do I eliminate the extra title bar?

To solve the window decorator issue, simply run the following in the terminal or Alt+F2 and the window decoration will immediately disappear:

gconftool-2 -s -t string '/apps/compiz-1/plugins/decor/screen0/options/decoration_match' '!state=maxvert'

Or just as @joschi's answer suggest, you can do that graphically using the CCSM:

I have set myself the 'decorations for windows' box to !(state=maxvert & state=maxhorz) because I do want the decorations when the window is only vertically/horizontally maximized (by clicking the maximize button with the middle/right button, respectively), and I do not want them if it is fully maximized.

You can try to change the settings in the 'Window decorations' option in CCSM. Type !state=maxvert in the 'decorations for windows' box which should remove the decorations of all maximized windows.