The Basel Committee promulgates bank regulatory standards that many major economies enact to a significant extent. One element of the Basel III capital standards is a system of capital surcharges for global systemically important banks (G-SIBs). If the purpose of the surcharges is to ensure the survival of G-SIBs through serious crises (like the 2007-09 financial crisis) without extraordinary public assistance, our analysis suggests that current surcharges are too low because of three shortcomings: (1) the Basel system underestimates the probability that a G-SIB can fail, (2) the Basel system fails to account for short-term funding, and (3) the Basel system excludes too many banks from current surcharges. Our best estimate suggests that the current surcharges should be between 225 and 525 basis points higher for G-SIBs that are not reliant on short-term funding; G-SIBs that are reliant on short-term funding should have even higher surcharges. Furthermore, we find that, even with significant confidence in the effectiveness of other Basel III reforms, modest increases in surcharges appear needed.