Hi,
A clean way is to autohide top and bottom panels.
If you want to autohide top and bottom panels in gnome-fallback please run dconf-editor and go to org.gnome.desktop.gnome-panel.layout.toplevels and there you will find top-panel and bottom-panel settings.
A dirty hack is to remove gnome-panel from /usr/share/gnome-session/sessions/gnome-fallback.session file. Using that you will remove both panels but you won't have as an example ALT+F2 run dialog available. Please notice that using this hack it isn't d-u safe.
You know what fits better your's needs.
Greets
convbsd