The purpose of this study is to explore the trade-off between technical efficiency and the quality of hospital services when the state is the sole provider. Data from 20 New Zealand District Health Boards from 2011 to 2017 is used to estimate technical efficiency using the data envelopment analysis technique, which employs an additive inverse formulation for undesirable outcomes. The estimated average quality-adjusted technical efficiency score is 0.69. In comparison, when the quality variable was removed, the efficiency declined to 0.66. More importantly, the ranking of district health boards stays consistent across both models, indicating that there is very little trade-off between quality and efficiency. A sensitivity analysis also confirms the lack of a trade-off between quality and efficiency.