Over the past decade several countries, including the US, have introduced or redesigned legislation that confers priority in bankruptcy upon all or some bank deposits. We argue that in the presence of contracting costs such rules can increase efficiency. We first show in a private information model that a borrower can reduce overall costs of finance by letting informationally heterogeneous lenders choose between junior and senior debt. In particular, we find that debt priorities reduce socially wasteful information gathering by investors. We then argue why, particularly in banking, legal standardization of debt priorities may be superior to bilateral private arrangements.