  We identify a subclass of the regular commutative languages that is closed
under the iterated shuffle, or shuffle closure. In particular, it is
regularity-preserving on this subclass. This subclass contains the commutative
group languages and, for every alphabet $\Sigma$, the class
$\textbf{Com}^+(\Sigma^*)$ given by the ordered variety $\textbf{Com}^+$. Then,
we state a simple characterization when the iterated shuffle on finite
commutative languages gives a regular language again and state partial results
for aperiodic commutative languages. We also show that the aperiodic, or
star-free, commutative languages and the commutative group languages are closed
under projection.
