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This study describes power-elastic systems, a method for designing systems whose operations are limited by applicable power. Departing from the traditional low-power design approach which minimises the power consumption for given amounts of computation throughput, power-elastic design focuses on the maximally effective use of applicable power. Centred on a run-time feedback control architecture, power-elastic systems manage their computation loads according to applicable power constraints, effectively viewing quantities of power as resources to be distributed among units of computation. Concurrency management is demonstrated as an effective means of implementing such run-time control, through both theoretical and numerical investigations. Several concurrency management techniques are studied and the effectiveness of arbitration for dynamic concurrency management with minimal prior system knowledge is demonstrated. A new type of arbitration, called soft arbitration, particularly suitable for managing the access of flexible resources such as power, is developed and proved.