I’ve read (oh lord, was it on here? I’m not a real member anymore so I don’t think I can check) that I can decaffeinate my own tea, to a degree, by emptying the water after about a minute then refilling. How does this work? Does the caffeine bind to water more readily than, um, the flavour (and, apparently, antioxidants)?
I’ve run across the same thing and wondered about it too.
A bit of googling shows that caffeine is not very soluble in water at room temperature but is highly soluble in boiling water. So if you steep the leaves in boiling (or just boiled I should say) water a larger portion of the caffeine will come out in the first 30 seconds or so. Whether or not you’d wash away antioxidants I don’t know-depends on their water solubility I guess.
It’s been a lot of years since organic chemistry unfortunately. 
I dont recall the specifics, but I remember running an experiment in highschool in which we purified the caffeine in a thing of tea. Seemingly you could do this at home with the right equipment. The authorities might think your running a meth lab though
This page claims that
My own experience using this method is that, yes, I did get less of a buzz from tea brewed this way, but I could still feel the caffeine. If you’re very sensitive to caffeine, I’m not sure this method will be good enough for you.
When I tried this, I found the tea was a little more bitter has more of a tannin bite and there seemed to be less of the more “flowery” aromas. As a point of reference, this was with loose leaf Darjeeling teas.
On that same page, there’s also information about the chemicals used to commercially decaffeinate tea. I’m guessing that methylene chloride isn’t something an amateur should be messing with, though…