We consider streaming of pre-encoded and packetized media over best-effort networks in presence of acknowledgment feedback. Given an estimation of future transmission resources and knowing about past transmissions and received acknowledgments, a scheduling algorithm is defined as a mechanism that selects the data to send over the network at any given time, so as to minimize the end-to-end distortion. Our work first reveals the suboptimality of popular greedy schedulers, which might be strongly penalized by anticipated retransmissions. It then proposes an original scheduling algorithm that avoids premature retransmissions, while preserving the simplicity of the greedy paradigm. The proposed patient greedy (PG) scheduler appears to save up to 50% of rate in comparison with the conventional greedy approach.