Oh bah, sorry Fidelia, I thought I posted a response to this. I swear I doctored one up in my email...
Several sessions of IPL is good for overall melasma. Fraxel or 'fractionalized C02' is the strongest overall laser for melasma but it's more expensive, painful, and requires more downtime. Actually full on C02 laser is best for blasting away moles and for serious resurfacing but for melasma might be too much. You will need more than one session of any laser (except maybe for the full on C02 laser which just blasts your skin away) and apply SPF religiously afterwards.
One point of confusion is that amongst different kinds of lasers, there are different *brands* of lasers. That's when things get more confusing, because sometimes when people mention a laser, they are referring to the specific brand.
I would recommend you schedule at least 3 consultations at doctor's offices, dermatologists, and medi-spas to see what they tell you. Then look up the info on the internet to see what you find about the lasers they recommend. Realself.com is a good review site by patients and also has doctor responses to questions.
I know for myself, I kept hearing the same recommendations over and over and did my research so I just went with it and I'm glad that I did.
Please keep us in the loop! And I'll do the same. :P I did two rounds of IPL and a Jessner's peel recently and I can see a difference in my melasma. BTW, it was my internist (not a derm) who told me I had melasma. I don't think I have medical melasma, just a lot of mottled discoloration that is the aftermath of acne (damn you genetics!). If your melasma is just on your upper lip, you can probably save a lot of money by asking for the price for just that area, not your whole face.