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Information-theoretic capacity notions for a slotted Aloha random-access system are considered in this paper, as well as joint power and retransmission controls for this protocol. The effect of the bursty nature of the arrival and transmission process on the information-carrying capability and spectral efficiency of the system is studied. The nature of the random-access protocol used to resolve decoding failures determines the system stability and dynamics, and in consequence its capacity. System control is carried out by dynamic control of retransmission probability and by power control. It is shown that substantial performance improvements can be achieved under this control scheme in terms of throughput and spectral efficiency for a range of channel parameters. The tradeoffs involving coding rate, system throughput, and spectral efficiency are analyzed from an information-theoretic point of view.