Does the EU have enough leverage to police the rule of law in Member States? This article first outlines how the infringement procedure is functionally adequate to address breaches of the rule of law. It argues that EU law entails “structural obligations” for Member States to uphold the rule of law within their legal systems. To the extent respecting such structural obligations is indispensable for observing specific EU law rules, their breach can be the target of infringement proceedings. The article then analyses the EU’s leverage to guarantee the authority of EU law in case of Member States’ non-compliance with fines imposed in that procedure. The article concludes that the recovery of fines by set-off against EU money enables effective policing if respect for the rule of law is deficient, and constitutes, therefore, an essential constitutional guarantee of the EU legal order.