Consider a setting where Willie generates a Poisson stream of jobs and routes them to a single server that follows the first-in first-out discipline. Suppose there is an adversary Alice, who desires to receive service without being detected. We ask the question: what is the amount of service that she can receive covertly, i.e. without being detected by Willie? In the case where both Willie and Alice jobs have exponential service times with respective rates µ 1 and µ 2 , we demonstrate a phase-transition when Alice adopts the strategy of inserting a single job probabilistically when the server idles : over n busy periods, she can achieve a covert throughput of O(√ n) when µ 1 < 2µ 2 , O(n/ log n) when µ 1 = 2µ 2 , and O(n µ2/µ1) when µ 1 > 2µ 2. When both Willie and Alice jobs have general service times we establish an upper bound for the amount of service Alice can get covertly. This bound is related to the Fisher information. Additional upper bounds are obtained for more general insertion policies.