A Q-Switched YAG laser has the ability to operate at different wavelengths with different components on the actual hand-piece. Blue, green, teal and yellow do require special attention, and can take longer, but yes, it can all be removed.
I'd venture to say that 3 treatments isn't enough to really gauge, most full removals can take a minimum of 10 treatments, perhaps longer.
Avoid showers or water for at least 8 hours after treatment, we also suggest leaving the skin exposed for at least an hour, to help dissipate heat, unless there is pinpoint bleeding. Drink lots of water, having laser treatments will dehydrate you. We suggest Aquaphor applied liberally for a minimum of 2-3 weeks, washing with warm soap and water and patting dry. If the treated area is somewhere that will come in contact with clothing or a high wear area, say your lower back, wrap in plastic wrap after applying Aquaphor.
For blisters, which should be somewhat rare, do not pop. Keep applying Aquaphor, drink water and they should heal on their own. If you get any scabs, that means you aren't hydrated enough and aren't using enough Aquaphor. In any event, never, ever pick at scabs if they do form. If you have an itch, lightly smacking the area will help. Again, itching indicates the skin isn't hydrated enough.
4-6 weeks, but everyone is different. At 6 weeks you may still not be ready for another treatment, every person is different. You'll also see more fading the longer you wait. For the cover up, I'd suggest 8-12 weeks between your last laser treatment and your first tattoo session.
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No, the laser does not "cut" skin - however pinpoint bleeding is always a possibility. The laser operates on wavelengths of light that target the pigment in your skin.
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To help avoid those scabs, keep a thick coating of Aquaphor on your treated area for 2-3 weeks, wrap in plastic wrap for sleeping and if clothing will be rubbing against the area.