What is the Best Way to Treat Deep Wrinkles Under the Eyes?

  I think either of the options you listed might be beneficial, and I would bet that the TCA peel would cost substantially less.  That said, without photos, it is hard to be sure if these are your best options.  Good luck!

Deep wrinkles under the eyes can be due excess skin laxity or loss of volume under the eyes.  Your non-surgical options include some form of skin resurfacing such as peels or lasers (consider fraxel CO2) and/or the addition of fillers such as Restalyn or Juvederm.  In addition, you might get some additional deeper tightening using Ultherapy under the eyes.

If there is a heavy amount of skin laxity, then I would consider a lower lid blepharoplasty where some of the skin is directly excised and the incision hidden under the margin of the lid.  This will give you the most flexibility to remove the wrinkles.  Volume loss can also be addressed by fat repositioning or fat grafting.

Good luck.

I agree with the other doctors on here that without a picture it is hard to give a definitive answer.  Typically I use a combination of fractional CO2 laser and dermal filling agents to address lines under the eyes.  Botox may also be used around and below the eye to further soften lines and open up the eyes.  If there is significant laxity to the skin, however, then a surgical intervention with or without laser may be the best option.  Good luck.