The recent financial turmoil has triggered a credit crunch whereby illiquid, but not necessarily insolvent, banks were not able to borrow money and were forced to be liquidated, bought or bailed out. A response to this problem has been contingent convertible bonds (or CoCo bonds), which are ordinary bonds that are converted into equity when certain financial triggers, such as capital ratios of banks, are reached. These have the potential of providing an automatic source of liquidity without having to go through bankruptcy or getting bailouts’ money. We present a model of liquidity with two types of investors who have different information about risk; one group has better information but a less elastic supply of funds, and the other produces liquidity via an elastic supply of funds but with much less information. The model generates a critical value of overall risk, above which there are “flights to quality” by liquidity suppliers. This leads to a sharp increase in borrowing costs for banks even though the underlying increase in risk is small. We next show that the existence of CoCo bonds can help to reduce the magnitude of a large and abrupt shift of credit dry-up from a relatively stable level.