Non-$n$-ampleness as defined by Pillay  and Evans  is preserved under analysability. Generalizing this to a more general notion of $\Sigma$-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis  for types of finite SU-rank. This is then applied to the special case of groups.
"Ample thoughts." J. Symbolic Logic 78 (2) 489 - 510, June 2013. https://doi.org/10.2178/jsl.7802080