In this paper, a novel cross-layer Adaptive Modulation and Coding scheme that optimizes the overall packet loss (by both transmission errors and excessive delays) probability under a given arrival process is developed. To this end, an improved Large Deviations approximation for the fraction of packets that suffer from excessive queuing delay is proposed. This approximation is valid for G/G/1 queues with infinite buffers that are driven by stationary arrival and service processes which satisfy certain conditions. Such models can capture the time correlations in the amount of traffic generated by streaming media sources and the time varying service capacity of a wireless link. Through numerical examples, the proposed AMC policy is shown to achieve a significant reduction in the overall packet loss rate compared to previously proposed schemes. This algorithmic performance gain can be translated into a sizeable decrease in the required transmit power or an analogous increase in the rate of the arrival process, subject to a given maximum packet loss rate Quality of Service constraint. Furthermore, the proposed AMC policy can be combined with ARQ in order to achieve an even lower overall packet loss probability.