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Anantharam. and Verdu (1996) introduced the exponential server timing channel (ETC) and determined that its capacity equals e-1μ nats/sec. More recently, Sundaresan and Verdu (2000) considered sequential decoding for this channel and found that its cutoff rate R0 is at least e-1μ/2. We show that R0=μ/4. We also determine the reliability exponent E(R) of the ETC for all rates between a "critical" rate Rc=(μ/4) ln 2 and the channel capacity C=e-1μ. We show that, for R≥Rc, E(R) coincides with the reliability exponent for the ideal photon channel (IPC).