Data Envelopment Analysis (DEA) based cost norms have attractive properties in the regulation of natural monopolies. However, they are also sensitive to the choice of cost drivers. When some of the cost drivers are discretionary, this may lead to suboptimal incentives. When a regulated firm compares the marginal change in its cost norm with its marginal cost of changing the discretionary output, the gains from adjusting the output will be very context specific. It is therefore unlikely that the regulation will induce socially optimal output levels. In this paper, we analytically and numerically examine the impacts of including a discretionary quality indicator in the benchmarking model used to regulate Danish water firms. We show that the eight-year catch-up period allowed in this regulation gives strong incentives to reduce costs since the firms can keep possible cost reductions for several years before the cost norm fully internalizes the cost reduction potentials. On the other hand, this scheme also provides very weak quality incentives since it takes eight years before the extra cost of increasing quality is fully internalized in the cost norm.