Supplementing the discussion in our book The Bankers’ New Clothes: What’s Wrong with Banking and What to Do about It, this paper examines the plausibility and relevance of claims in banking theory that fragility in bank funding is useful because it imposes discipline on bank managers. The assumptions about information and about costs of bank breakdowns underlying these claims are unrealistic and they cannot be generalized without undermining the theory and policy prescriptions. The discipline narrative is also incompatible with the view that deposits and other forms of short-term bank debt contribute to liquidity provision; in this liquidity narrative, the fragility of banks is a by-product of useful liquidity provision and can only be avoided by government support. We contrast both narratives with an explanation for banks’ avoidance of equity and reliance on short-term debt that appeals to debt overhang and government guarantees and subsidies for debt. In this explanation, the fragility of banks arises from conflicts of interest and is neither useful for society nor unavoidable.