A single-input-single-output (SISO) Poisson fading channel with perfect channel state information (CSI) at the transmitter and the receiver is considered. For a fixed basic rate r 0 , a service outage occurs when the instantaneous transmission rate falls below the rate r 0 . The objective of this paper is to maximize the expected transmission rate subject to peak and average transmitter power constraints and a constraint on the service outage probability. The optimal power allocation scheme is shown to be a combination of the ergodic capacity-achieving power allocation and the outage capacity-achieving power allocation schemes with a randomization between the two deterministic schemes in a boundary set. This randomization is not necessary when the channel fade distribution is continuous. By combining the concepts of ergodic and outage capacity, the proposed optimal scheme judiciously resolves the conflicting objectives of high expected transmission rate and low outage probability.