  This paper explores the following regularity properties and their
relationships for simple, not-necessarily-unital C*-algebras:
  (i) Jiang-Su stability,
  (ii) Unperforation in the Cuntz semigroup, and
  (iii) slow dimension growth (applying only in the case that the C*-algebra is
approximately subhomogeneous).
  An example is given of a simple, separable, nuclear, stably projectionless
C*-algebra whose Cuntz semigroup is not almost unperforated. This example is in
fact approximately subhomogeneous. It is also shown that, in contrast to this
example, when an approximately subhomogeneous simple C*-algebra has slow
dimension growth, its Cuntz semigroup is necessarily almost unperforated.
