To address the challenges posed by global systemically important banks (G-SIBs), the Basel Committee on Banking Supervision recommended an “additional loss absorbency requirement” for these institutions. Along these lines, I develop a microfounded design of capital surcharges that target the interconnectedness component of systemic risk. These surcharges increase the costs of establishing interbank connections, which leads to a non-monotonic welfare effect. While reduced interconnectedness decreases welfare by restricting the ability of banks to insure against liquidity shocks, it also increases it by reducing contagion when an interconnected bank fails. Thus, the regulator faces a trade-off between efficiency and financial stability. Furthermore, I show that capital requirements are more effective than default fund contributions when tail-risk exposure is the private information of banks. I conclude by analyzing how resolution regimes and stable funding requirements interact with these surcharges.