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I happened to be a but of a specific kind of laser buff. Um, as far as tria laser hair removal goes, it's kinda garbage for a few reasons.
it's an LED Diode laser. I don't think they are being entirely honest, or at least they're exaggerating their clinical trial results. It's NM is fairly normal, and watt strength. Honestly, though it's not going to be nearly as effective as the Silk'N line of products. (it's the best of what I've research for home hair removal based one product availability, technical specs, long lasting effects, ect.
To answer you question though, no, Tria will not do that on your upper lip, unless you either have coarse hair like a man, or dark hair and a medium skin tone. It will also not do that in two treatments. No hair removal treatment can do that. (Not even professionally!)
Follicles may not all be on the same growth cycles, when you decide to do a laser treatment either at home, or professionally. This means you shouldn't expect all of the hair to be uniformly vaporized. It will most likely be patchy until you get the rest of the hairs. When you do manage to get each one, they don't vanish, but instead, it is a slow reduction of the thickness of the hairs, and the quantity. If you're lucky, it slows down to a halt to where only once in a while you need to touch up with your home laser device, but that's with SEVERAL sessions. The only reason why you would want to purchase one of these devices, is because you go through the hell of shaving anyway, and there may be an end if you're genetically lucky!
Well permanent really depends on you, if you use it for at least 2 yrs, in the areas it will actually read the hairs, and, permanent, I mean, well nothing is permanent, but this still beats shaving daily for the rest of your life, so what if every 2 years you have to spend 3-4 months doing touch ups (maybe?)
I would suggest right now the silk'n line, specifically the Silk'N SensEpil. The newer one they have of the sensepil is just a color change. Anyways their lasers are a bit different then what else is available for home use, and I would highly recommend it if you want the best, fastest, and long lasting results. The only drawback is you have to buy cartriges but, consider the end game.
I should note... Just in case I wasn't clear. In office is superlative to at home laser treatments. By far. ummm. I just like having the up keep maintenance in an at home laser to slowly trim away at "grow backers.". (In fact I was thinking about building my own home hair removal laser.)