  We show that for a large class of C*-algebras $\mathcal{A}$, containing
arbitrary direct limits of separable type I C*-algebras, the following
statement holds: If $A\in \mathcal{A}$ and $B$ is a simple projectionless
C*-algebra with trivial K-groups that can be written as a direct limit of a
system of (nonunital) recursive subhomogeneous algebras with no dimension
growth then the stable rank of $A\otimes B$ is one. As a consequence we show
that if $A\in \mathcal A$ then the stable rank of $A\otimes\mathcal W$ is one.
We also prove the following stronger result: If $A$ is separable C*-algebra
that can be written as a direct limit of C*-algebras of the form
$\mathrm{C}_0(X)\otimes \mathrm{M}_n$, where $X$ is locally compact and
Hausdorff, then $A\otimes \mathcal W$ can be written as a direct limit of a
sequence of 1-dimensional noncommutative CW-complexes.
