The apparent banking market failure modeled by Diamond and Dybvig [1983] re
sts on their inconsistently applying their "sequential servicing constraint
" to private banks but not to their government deposit insurance agency. Wi
thout this inconsistency, banks can provide optimal risk-sharing without ta
x-based deposit insurance, even when the number of "type 1" agents is stoch
astic, by employing a "contingent bonus contract." The threat of disinterme
diation noted by Jacklin [1987] in the nonstochastic case is still present
but can be blocked by contractual trading restrictions. This article comple
ments Wallace [1988], who considers an alternative resolution of this incon
sistency.