Solutions to valid Quantified Constraint Satisfaction Problems (QCSPs) are called winning strategies and represent possible ways in which the existential player can react to the moves of the universal one to “win the game”. However, different winning strategies are not necessarily equivalent: some may be preferred to others. We define Quantified Constraint Optimization Problems (QCOP) as a framework which allows both to formally express preferences over QCSP strategies, and to solve the related optimization problem. We present examples and some experimental results. We also discuss how this framework relates to other formalisms for hierarchical decision modeling known as von Stackelberg games and bilevel (and multilevel) programming.