Caico-Thyroid Approximation. VFS involves no external cuts however if your voice was damage as the result of a trachea shave, CTA will repair the damage and will remove additional material if needed. VFS can only provide about a 80 HZ improvement at best and depending on how much damage the trachea shave did, CTA may not be an option to correct your voice. Dr Haben will need to make the final determination in person.
Dr Haben will look out for your best interest. I expected to be told I would need CTA but Dr Haben determined it wasn't needed in my case. He was a bit conservative estimating my gain but I did better than expected and hit the golden 220 Hz mark.
The link in the above post provide a detail description of the procedures that Dr Haben uses. VFS is done by other surgeons and the basic concept is the same but their procedures may be different.