Lower Lip Lift to Correct Lower Tooth Show

Is there a procedure, besides injectables, to raise the lower lip higher on the lower gum line, or to pull it in closer to the lower gums. I would think you could cut and reattach. I do not know how far down is the "norm" for the lower lip to attach to the gum, but my lower lip droops down and shows too much of my lower teeth when my face is relaxed.Injectables in my opinion would only increase the weight of the lower lip and make it droop more. My bottom lip is quite full already.