Environmental policies often include exemptions for some firms, e.g. the smallest emitters. This text explores the implications of such exemptions in the case of an emission tax, and in the presence of monitoring, reporting, and verification (MRV) costs. We develop an analytical framework capturing the trade-off between the cost-effectiveness of a broader tax base, and the savings on MRV costs enabled by a partial coverage. We characterize the optimal threshold below which firms should be exempted. Since determining this threshold is demanding in terms of information regarding firm-level MRV and abatement costs, we propose a simple approximation requiring knowledge of these costs only at the aggregate level. We apply this framework to assess the welfare implications of such an instrument in the case of greenhouse gas emissions from European agriculture. The findings indicate that exempting the smallest emitters may provide significant savings on MRV costs compared to the full coverage, while still incentivizing cost-effective reductions in emissions.