Energy harvesters are widely used to power wireless sensor systems, but the produced power is generally low, and can vary abruptly due to changes in the environment or the device's location. Energy buffers (batteries or supercapacitors) are normally incorporated into systems to smooth out these variations. However, they have a limited lifetime and increase system size and cost. Transient computing aims to address these issues by removing the energy buffer, and powering the system directly from the energy harvester. Approaches such as Hibernus++ deal with the resultant power intermittency by 'hibernating', i.e. saving a snapshot of the system state to non-volatile memory before a power failure, and restoring it after the power recovers. The overheads of this can be particularly costly with a low-current harvester, as the system may wake up and hibernate at a high frequency, doing little useful work in each power cycle. This paper proposes an enhancement to these approaches, providing an efficient method to avoid repeated hibernation. The introduction of a 'sleep' state, which is entered when the power supply is detected to be failing, allows the system's supply voltage to recover without taking a snapshot. Thus, the application can spend more time on useful work rather than checkpointing. If the supply voltage continues to decline, a snapshot will then be taken. The approach has been simulated and experimentally validated, with results demonstrating that the proposed scheme provides up to a 65% improvement in system active run-time with low-current harvesters vs. conventional Hibernus++.