  We study avoidability of collections of balls in bounded $C^{1,1}$ opens sets
for censored $\alpha$-stable processes, $\alpha\in (1,2)$. The results are
analog to the ones obtained for Brownian motion in S. J. Gardiner, M. Ghergu,
Champagne subregions of the unit ball with unavoidable bubbles, Ann. Acad. Sci.
Fenn. Math. 35 (2010) 321-329. On the way we derive a Wiener-Aikawa-type
criterion for minimal thinness with respect to the censored stable processes.
