This paper investigates adaptive streaming codes over a three-node relayed network. In this setting, a source transmits a sequence of message packets through a relay under a delay constraint of $T$ time slots per packet. The source-to-relay and relay-to-destination links are unreliable and introduce a maximum of $N_1$ and $N_2$ packet erasures respectively. Recent work has proposed adaptive (time variant) and nonadaptive (time invariant) code constructions for this setting and has shown that adaptive codes can achieve higher rates. However, the adaptive construction involves high computational complexity and large block lengths. In this work, we propose a simplified adaptive code construction which greatly improves the practicality of the code, with only a small cost to the achievable rates. We analyze the construction in terms of the achievable rates and field size requirements, and perform numerical simulations over statistical channels to estimate packet loss probabilities.