  We consider a class of planar dispersing billiards with a cusp at a point of
vanishing curvature. Convergence to a stable law and to the corresponding
L\'evy process in the $\cM_1$ and $\cM_2$ Skorohod topologies has been studied
in recent work. Here we show that certain sufficient conditions for
$\cM_2$-convergence are also necessary.
