||Systemic risk is, by nature, unpredictable. Statistical models can fail to identify it. We need to maintain resource buffers as well as to implement better regulatory controls, and to improve managerial experience, and contingent strategies. International imbalances are nearly up to their sustainable limits, creating new systemic challenges. Some major financial institutions have recently assumed a critical position: they are highly interconnected and hard to replace in a panic. These institutions play key roles in the economy, such as providing market liquidity and pricing assets efficiently. Following deregulation, these institutions became “universal” groups covering a large range of financial markets and products. Internal conflicts of interest, opacity, and manipulated risk measures may arise. Regulation must change and new market instruments could exacerbate these internal problems. Here, we discuss some proposals to enhance the role of the Resolution Authorities (American and European laws are in the process of defining them). In particular, we examine a proposal for high-trigger contingent convertible bonds (HT CoCos), especially conceived for Systemically Important Financial Institutions – SIFIs (Calomiris and Herring, 2011).We propose that the bond conversion should be applied to all SIFIs’ HT CoCos as soon as one SIFI defaults. This solution could have many advantages: less costly recapitalization of the SIFIs’ system, more level playing field in the financial industry, good incentives to shareholders and supervisors to react promptly to potential systemic crisis, introducing breaks in SIFIs’ market values correlation (and with Sovereigns, too). We also provide a quantification of the potential market for such instruments.