  We construct Z^2-SFTs at every computable level of the hierarchy of
topological completely positive entropy (TCPE), answering Barbieri and
Garc\'{i}a-Ramos, who asked if there was one at level 3. Furthermore, we show
the property of TCPE in Z^2-SFTs is coanalytic complete. Thus there is no
simpler description of TCPE in Z^2-SFTs than in the general case.
