  We study minimal thinness in the half-space $H:=\{x=(\wt{x}, x_d):\,
\wt{x}\in \R^{d-1}, x_d>0\}$ for a large class of rotationally invariant L\'evy
processes, including symmetric stable processes and sums of Brownian motion and
independent stable processes. We show that the same test for the minimal
thinness of a subset of $H$ below the graph of a nonnegative Lipschitz function
is valid for all processes in the considered class. In the classical case of
Brownian motion this test was proved by Burdzy.
