  The Quantified Constraint Satisfaction Problem is the problem of evaluating a
sentence with both quantifiers, over relations from some constraint language,
with conjunction as the only connective. We show that for any constraint
language on a finite domain the Quantified Constraint Satisfaction Problem is
either in $\Pi_{2}^{P}$, or PSpace-complete. Additionally, we build a
constraint language on a 6-element domain such that the Quantified Constraint
Satisfaction Problem over this language is $\Pi_{2}^{P}$-complete.
