Issues on service quality are crucial for water utility management and regulation. Omitting these aspects can lead to important biases in estimating costs of services. In our article, we integrate in a translog cost model variables proxying the output multi-dimensionality. We test and consider endogenous output quantity and quality. The scale issues and performance effects of public vs. private ownership are investigated with the objective of evaluating how the introduction of the quality dimension may affect them. Cost model is estimated by GMM from a dataset of the U.S. water utilities. It is shown that the inclusion of quality level of the delivered services has a significant impact on estimation results.