Recent treatments of the issue of a zero floor on nominal interest rates have been subject to some important methodological limitations. These include the assumption of perfect foresight or the introduction of the zero lower bound as an initial condition or a constraint on the variance of the interest rate, rather than an occasionally binding non-negativity constraint. This paper addresses these issues offering a global solution to a standard dynamic stochastic sticky price model with an explicit occasionally binding non-negativity constraint on the nominal interest rate. It turns out that the dynamics and sometimes the unconditional means of the nominal rate, inflation and the output gap are strongly affected by uncertainty in the presence of the zero lower bound. Commitment to the optimal rule reduces unconditional welfare losses to around one-tenth of those achievable under discretionary policy, while constant price level targeting delivers losses which are only 60% larger than under the optimal rule. Even though the unconditional performance of simple instrument rules is almost unaffected by the presence of the zero lower bound, conditional on a strong deflationary shock simple instrument rules perform substantially worse than the optimal policy.