On the one hand it's simple: Tier 0 is pretty much like SingleZeta, but better optimized, then in Tier 1 we add one more orbital, viz. the one that gives the best improvement of the total energy, and then we keep adding. The method follows that of (ref to be added, I forgot it)
That said, the current tier basis sets shipped with ATK are not perfect. They are fitted only to dimers, which is a bit too restricted. So, I would put up a small warning flag for them, esp. some are know to be rather bad (like Oxygen). Although, some are really good, like Germanium and Vanadium. So, before using any of these basis sets (well, before using any basis set) you should check its properties by at least running some tests on basic systems like elemental crystals etc and compare to known results.
We are working on improving the algorithm and the basis sets and hope to have updated sets soon.
