For more than fifteen years, researchers have tried to support global optimizations
in a usable semantics for a concurrent programming language, yet this task has been
proven to be very difficult because of (1) the infamous ``out of thin air'' problem,
and (2) the subtle interaction between global and thread-local optimizations.

In this paper, we present a solution to this problem by redesigning a key
component of the \emph{promising semantics} (PS) of Kang et al.
Our updated PS 2.0 model supports all the results known about the original
PS model (\textit{i.e.}, thread-local optimizations, hardware mappings, DRF theorems),
but additionally enables transformations based on global value-range analysis
as well as register promotion (\textit{i.e.}, making accesses to a shared location local
if the location is accessed by only one thread).
PS 2.0 also resolves a problem with the compilation of relaxed RMWs to ARMv8,
which required an unintended extra fence.