There is a simple and a more complicated way to address this.
For mild to moderate drooping, and assuming that a patient is not interested in surgery, one can use a filler (Radiesse or Juvederm) to provide volume to the oral commissure (corner of the mouth), combination to a small amount of Botox to the DAO's (muscle that pulls the corner of the mouth down). This is a temporary solution.
Assuming you are willing to have surgery and you have further indications (jowls and changes to the neck), a Facelift may address some of your concerns. However, it is important to note that too much tension on the corners of the mouth is one of the tell tale signs of an overdone Facelift.



