Environmental incentives are characterized by two distinct features: (1) a benefit-cost trade-off; and (2) private information about the trade-off. This suggests a degree of freedom of where to attach the private information, either to the benefit or the costs, as long as these choices imply the same behavior absent incentives (‘observation equivalent’). However, we show that different observation equivalent specifications can lead to different incentives. This is demonstrated for two cases: rainforest protection and contributions to a public good. Therefore, the choice of a private information parameter must be justified against observation equivalent alternatives.