What is the best procedure to address marionette lines? Is DAO release surgery the best option? (photos)

I'm 45 years old & have deep lines at the corners of my mouth. I searched before and after photos and found a surgeon whose patients seemed to have improved marionette lines after his face-lift. I traveled to this surgeon who performed a deep plane face lift & chin implant. It has been 7 months. My face looks better but there is very minimal improvement to my marionette lines which was my main concern. Is there a procedure that will help with this?