Botox on the Depressor Anguli Oris Muscle?

You are correct, a small amount of Botox into the DAO muscle can diminish the downward pull on the corners of the mouth and allow the muscles that elevate the corners to take over. I would suggest trying that first and waiting about 2 weeks to assess the results. If more correction is needed, you can have filler like Restylane  placed. The risk of incorrect placement of Botox is an irregular smile or even oral incompetence. Therefore, it is crucial that you are injected by a well-trained individual.

Be sure to discuss your treatment with a well-trained and reputable provider for best results. Treating the DAO's will relax the muscles and won't allow you to purposefully make the down-turn of the corners of your mouth. Treatment is typically conservative. If the injections are not in the proper muscle or too aggressive, you'll have issues with your bottom lip and could have an unnatural look and feel until the product wears off.