Levi problem and semistable quotients

A complex space $X$ is in class ${\mathcal{Q}}_G$ if it is a semistable quotient of the complement to an analytic subset of a Stein manifold by a holomorphic action of a reductive complex Lie group $G$. It is shown that every pseudoconvex unramified domain over $X$ is also in ${\mathcal{Q}}_G$.