  We introduce the notion of an NTP$_{2}$-smooth measure and prove that they
exist assuming NTP$_{2}$. Using this, we propose a notion of distality in
NTP$_{2}$ that unfortunately does not intersect simple theories trivially. We
then prove a finite alternation theorem for a subclass of NTP$_{2}$ that
contains resilient theories. In the last section we prove that under NIP, any
type over a model of singular size is finitely satisfiable in a smaller model,
and ask if a parallel result (with non-forking replacing finite satisfiability)
holds in NTP$_{2}$.
