Harvesting energy from environments has been a promising approach to power ubiquitously distributed Internet of Things (IoT) devices. For harvesting kinetic energy with piezoelectric transducers, synchronized switch harvesting on capacitors (SSHC) rectifiers have been demonstrated to achieve high energy extraction performance without using any inductor. In previous studies, the switched capacitors in SSHC rectifiers are chosen equal to the inherent capacitance of the piezoelectric transducer (PT) to achieve good voltage flip efficiencies at 33.3%, 50% and 66.7% for 1-, 2- and 4-stage SSHC rectifiers, respectively. However, with much larger switched capacitors and the same SMD package size, this paper finds that the voltage flip efficiency can be further increased to 50%, 66.7% and 80% for 1-, 2- and 4-stage SSHC rectifiers, respectively; as a result, the output power can be greatly increased. This paper also finds that the proposed design only requires half number of capacitors to achieve the same voltage flip efficiency for conventional SSHC rectifiers, which significantly reduces the system form factor for miniaturization.