Bohm (1982) reported a Swedish census project, which used a cost-sharing mechanism giving participants incentives to misrepresent their willingness to pay (WTP), yet still ended up providing a public good. In this paper we offer a theoretical analysis of the mechanism and propose two revisions. In the first revision, the incentives to overstate or understate are randomized, weakening participants’ tendency to misrepresent WTP. Whereas in the second revision, reporting true WTP is participants’ weakly dominant strategy. Our revisions delineate a simple approach to induce true WTP, while the Swedish mechanism can be treated as a special case.