A new procedure for handling retransmissions in a selective-repeat ARQ system is proposed. This procedure can operate with a receive buffer of minimal size; in addition it places little computational load on the transmit and receive processors. The procedure is simple enough that its throughput can be calculated exactly. Analysis of this strategy shows that: 1)it yields higher throughput than earlier ARQ techniques; 2) for modest receive buffer size, its throughput differs little from channel capacity; 3) as buffer size increases, throughput approaches channel capacity. The final section of the paper considers the performance of ARQ systems on channels in which errors occur in bursts. It indicates that on reasonably good channels, error burstiness has little effect on throughput.