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This might be a more interesting solution: http://sublimetext.userecho.com/topic/106652-/
I stopped using tabs in sublime (they are hidden) in favor of a combination of "Goto Anything..." + "next_view_in_stack/prev_view_in_stack".
The only 2 things missing are:
1. The name of the file being displayed. Would be nice to have an option to display the current file name in the status bar.
2. When browsing the views in the stack, a representation of the views, and an indicator of witch view is currently being displayed (pretty much like the application switcher in Windows, Ubuntu(alt+tab) or Mac OS X(cmd+tab)). This could be achieved with a palette containing the views in the stack, which gets dismissed when the modifier key (cmd/alt/ctrl) of the shortcut set to "next_view_in_stack/prev_view_in_stack" is released. http://sublimetext.userecho.com/topic/106652-/
Customer support service by UserEcho
With the gained space from the unification of the titlebar with the tabs, breadcrumbs could be added, which, beside having the function of showing you the path, could provide a quick access to folder and files.
If you don't need the quick navigation and want to keep the extra space, displaying the file path in the status bar (when there is no status message) could be a solution.