Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(√n) bits in n channel uses. However, this result is predicated on Willie having an accurate statistical characterization of the background noise. When Willie has uncertainty about his noise characteristics and his receiver is limited to a power detector, O(n) bits can be covertly delivered. Here, we establish covert communication of O(n) bits in n channel uses while: (i) generalizing the environment; and (ii) removing any restrictions on Willie's receiver. We consider the case where an additional node, called the "jammer", is present to help Alice and Bob communicate covertly. This jammer is termed "uninformed", as it does not know the content or timing of Alice's transmission. We consider both AWGN channels and a scenario with a block faded jammer with a single fade per codeword. In these scenarios, we are able to establish the optimality of the power detector for Willie, from which the achievability of reliable and covert communication at a positive rate follows.