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Electron acceleration in a one-dimensional plasma wave has been simulated, with emphasis on minimizing the energy spread of an accelerated electron bunch, while keeping the mean energy gain at a reasonable level. Bunch length, beam loading, and the injection phase are tuned to reach this goal. The simulation results show that, in a wide range of initial bunch lengths and beam loading parameters, an optimum acceleration distance exists, which combines low energy spread and high energy gain. The energy spread at the optimum is found to be weakly dependent on bunch length and beam loading, while it is highly sensitive to deviations in the injection phase.