Is there a procedure to fix a saggy top lip? (Photo)

I had oral surgery as a teen to reduce the gap between my front teeth. The small flap that runs between the lip and gums was clipped in the procedure (to eliminate the gap?). Now, my teeth are completely hidden by a flap that has been dropping further all the time. I would like to be able to smile and show my teeth, but that flap only hides when I roll my lip under.

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