I'm not sure if you've read our story about our daughter's nasal tip H, but if not here is the link. http://188.8.131.52/board/showthread.php?t=3666
We had great success with laser, despite the fact that we had both superficial and deep H as well. Also, our daughter never received any anasthesia. There is some pain, but it is over literally within seconds, and does not linger. Her total time out of our arms was ten minutes, the treatment was less than one minute, and by the time they gave her back to us she was usually not even crying.
We really highly recommend the laser, especially early on. That is the key for the laser. It stopped our daughters H from growing any further. She had her first treatment at eight weeks, and had a total of nine over the next eleven months. She's fifteen months soon and hasn't had one for over two months. We're hopeful she's done. Her nose looks great.
Anyway, best of luck to you. I hope you get the treatment that you want.