Weitzman (2002) studies the regulation of a fishery characterised by constant marginal harvest costs and shows that price regulation performs better than quantity regulation when the regulator is uncertain about the biological reproduction function (ecological uncertainty). Here, we initially illustrate that this result does not generalise to a search fishery, where marginal costs are allowed to depend on harvest. Hansen et al (2008) study a fishery where non-compliance with regulations is a problem. When the regulator is uncertain about non-compliance (compliance uncertainty), then landing fees are the preferred type of regulation, and Hansen et al (2008) find that this result does generalise to a search fishery where marginal costs depend on harvest. In this paper, we simulate a stochastic stock-recruitment model for the Danish cod fishery in the Kategat capturing both ecological and compliance uncertainty. We find that the gain from eliminating compliance uncertainty may be up to 5% of gross profit while the gain from eliminating ecological uncertainty is minimal. Under landing fee regulation, the entire gain from eliminating both types of uncertainty is captured, even if the regulator's stock measurement is uncertain. However, most of this gain can be captured within an ITQ system if the regulator is able to measure stocks accurately.