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Subthreshold operation is a promising method for reducing power consumption in ultra-low power applications, such as active RFIDs and sensor networks. It was shown in previous works that operating at the Vmin supply voltage results in optimal energy operation, where Vmin typically falls below the threshold voltage. However, all previous subthreshold analyses ignore the leakage current in standby mode. Hence, for applications where operation at Vmin results in completion of the task well ahead of the required deadline, the energy consumption can be significantly under-estimated In this paper, we investigate the effect of the non-zero standby energy on the optimal energy consumption in subthreshold operation. We first analyze energy consumption both with and without a cutoff technique in standby mode. Two parameters are proposed to capture the cutoff structure's effect on the energy consumption. Second, a methodology to minimize the total energy consumption is addressed The selection of the cutoff structure is examined by comparing three different structures. Then, a co-optimization method to optimize the size of the cutoff structure concurrently with the supply voltage, is proposed. This approach reduces energy by 99.2% compared to standby-energy-unaware optimization.