  Let $A$ be a separable (not necessarily unital) simple $C^*$-algebra with
strict comparison. We show that if $A$ has tracial approximate oscillation zero
then $A$ has stable rank one and the canonical map $\Gamma$ from the Cuntz
semigroup of $A$ to the corresponding affine function space is surjective. The
converse also holds. As a by-product, we find that a separable simple
$C^*$-algebra which has almost stable rank one must have stable rank one,
provided it has strict comparison and the canonical map $\Gamma$ is surjective.
