The current narrow banking proposal begins by observing that the magnitude of safe short term assets held outside the banking system exceeds the magnitude of banks' demand deposit liabilities and then argues problems associated with illiquid banking can be avoided by requiring demand deposits be backed by safe short term assets (see e.g. Wallace [1996]). In this paper it is established that, although inefficient, the observation of safe short term assets outside an illiquid banking system does not justify the introduction of narrow banking. It is shown that illiquid banking has the potential to improve welfare relative to direct investment in available assets (autarky) whereas narrow banking does not. It is also shown that an illiquid banking system, which includes a mechanism that facilitates the transfer of liquidity among banks, can always increase welfare relative to autarky and the outcome is efficient if the return on demand deposits is sufficiently high. Three policy implications for illiquid banking follow from the results obtained. One, design of the mechanism which facilitates the transfer of liquidity among banks is crucial. Two, restricting returns on demand deposits can be undesirable. Three, deposit insurance is not required to deal with the problem of uncertain withdrawals faced by individual banks.