A regulator imposes a universal service obligation (USO) on a vertically integrated firm that owns an essential network. The regulator has imperfect information about the network's fixed cost. Network access is provided to licensed competitors. The USO consists in a constraint on market coverage and is compensated through a mix of public funds and transfers from entrants. We first use a basic adverse selection model to show that, because of informational rents, a sufficiently high shadow cost of public funds can lead to a lower coverage with the USO than without it. We then show that this result tends to be robust in various realistic extensions of the basic model.