Using incentives to reduce consumption of scarce goods is a core tenet of environmental economics, but allowing prices to reflect scarcity can result in unpalatable distributional outcomes. Water utilities often adopt nonlinear rate structures to balance conservation and equity objectives. We investigate the performance of conservation pricing schemes within existing nonlinear rate structures implemented during severe drought conditions in Southern California. First, we estimate the demand response to conservation pricing using machine learning to generate counterfactual predictions. We identify only modest conservation effects attributable to conservation pricing directly, despite marginal prices rising by up to 400%. We then decompose who bears the burden of conservation pricing under nonlinear rates. Simpler rate structures perform better on equity dimensions with no serious implications for conservation. Overall, our results suggest that complicated nonlinear rates neutralize the effectiveness of conservation prices by shielding higher-consuming users from the highest marginal prices.