Given a cellular automaton $F:A^{\ZZ} \to A^{\ZZ}$, we define its
small quasi-attractor $\Qq_F$ as the nonempty intersection
of all shift-invariant attractors of all $F^q\sigma^p$, where $q>0$ and
$p\in\ZZ$. The measure attractor $\Mm_F$ is the closure of the supports
of the members of the unique
attractor of $F:\MMM_{\sigma}(A^{\ZZ}) \to \MMM_{\sigma}(A^{\ZZ})$ in the
space of shift-invariant Borel probability measures.