Share with me your wisdom, because I still end up paying out the nose abroad. Outside of dodgy methods and potentially risky tax havens, its pretty hard nowadays to hide money from Uncle Sam (see FATCA). The FEIE also doesn't count towards everything including FICA taxes (which you'll still end up paying $15.3k on that first $100k). Additionally, FATCA has made banking extremely difficult for Americans abroad, and is one major reason for a lot of citizens renouncing their US citizenship (year on year increases).
Combined with FATCA and being the only civilized country in the world to tax foreign earned income on non habitual residents, which in its own complicates tax returns and more headaches especially with countries that don't have double taxation agreements with the USA, you can see why people may consider renunciation.
To Bluematter:
I'm currently planning on moving my family to Valencia, Spain later this year. I'll look you up when I'm in town.
Nothing particularly clever - just bill revenue from an entity in a jurisdiction that has zero (or otherwise low) corporate tax rate.
To make it work in the big picture such that you'll end up with beneficial use and control of the assets, and particularly if you're a US citizen, you'll end up with a few different entities and one ultimate holding trust. Sounds far more complex than it actually is - if you're that way inclined, you can DIY for about $5-10k setup then $3-5k/year, or use a service provider to do it for you.
Apportioning revenue to favorable jurisdictions is exactly what the giants (Microsoft, Google, Apple, Amazon, Cisco, et al) do when operating in non-favorable jurisdictions - though they do it slightly differently through transfer pricing arrangements, but the effect is the same; the bulk of the revenue, and almost all of the profit, gets booked in no/low tax jurisdictions.
Anything you pay yourself as salary will still be taxable as personal income, so if you're earning <$100k it's not really worthwhile, but anyone talking about tax issues is presumably progressing well beyond that level.
PS - if you wanted to bill from a local company rather than an offshore company, you could do so, and set transfer pricing favorably. This is considerably more risky, because transfer pricing arrangements are the easiest things for local tax authorities to attack (because they're in a local jurisdiction), and as is the case in Australia, if the tax authorities simply 'deem' transfer pricing to have been structured in a manner other than fair market value arms length negotiations, they'll just retrospectively issue adjustments and bill you as though the revenues were earned in Australia. I'm sure the experts could give you lots of intelligent commentary on this, but this simple issue, from my perspective, makes billing from a local company significantly risky.