This paper investigates adaptive streaming codes over a three-node relayed network. In this setting, a source node transmits a sequence of message packets to a destination with help of a relay. The source-to-relay and relay-to-destination links are unreliable and introduce at most N_1 and N_2 packet erasures, respectively. The destination node must recover each message packet within a strict delay constraint T. The paper presents a new construction of streaming codes for all feasible parameters \N_1, N_2, T\. Our work improves upon the construction in Fong et al. by adapting the relaying strategy based on the erasure patterns from source to relay. Specifically, the code employs the notion of symbol estimates, which allows the relay to forward information about symbols before it can decode that symbol and variable-rate encoding, which decreases the rate used to encode a packet as more erasures affect that packet. The codes proposed in this paper achieve rates higher than the ones proposed by Fong et al. whenever N_2 > N_1 and achieve the same rate when N_2 \leq N_1 , in which case the rate is optimal. The paper also presents an upper bound on the achievable rate that takes into account erasures in both links in order to bound the rate in the second link. The upper bound is shown to be tighter than a trivial bound that considers only the erasures in the second link. © 1963-2012 IEEE.