  Let $A$ be a finite-dimensional self-injective algebra over an algebraically
closed field, $\mathcal{C}$ a stably quasi-serial component (i.e. its stable
part is a tube) of rank $n$ of the Auslander-Reiten quiver of $A$, and
$\mathcal{S}$ be a simple-minded system of the stable module category
$\stmod{A}$. We show that the intersection $\mathcal{S}\cap\mathcal{C}$ is of
size strictly less than $n$, and consists only of modules with quasi-length
strictly less than $n$. In particular, all modules in the homogeneous tubes of
the Auslander-Reiten quiver of $A$ cannot be in any simple-minded system.
