The maximum throughput of relaying information flows while concealing their presence is studied. The concealment is achieved by embedding transmissions of information flows into truly independent transmission schedules that resemble the normal transmission behaviors without any flow. Such embedding may reduce the throughput for delay-sensitive flows, and the paper provides a quantitative characterization of the level of reduction. Under a strict or average delay constraint, the maximum normalized throughput is measured by the efficiency of the optimal relay algorithms that embed the most flow into given transmission schedules. Exact analytical solutions and closed-form approximations are derived for renewal schedules, verified by simulations on both synthetic traffic and traces. The results reveal general relationships between the clandestine throughput and system parameters including delay constraints, traffic load, and traffic distributions. In particular, the throughput is found to be negatively related to the burstiness of the cover traffic. Moreover, simulations show that the throughputs of renewal traffic with certain powerlaw interarrival distributions can closely approximate those of actual traces.