To reduce the construction cost of the power-supplying infrastructure in data centers and to increase the utilization of the existing one, many researchers have introduced software-based or hardware-based power-capping schemes. In servers with consolidated virtual machines, which can be easily found in cloud systems, exporting virtual machines to other light-loaded servers through live-migration is one of the key approaches to impose power-capping on servers. Up until now, most researchers who have tried to achieve power-capping through live-migration assumed that exporting a virtual machine instantly reduces the server power consumption. However, our analysis introduced in this paper reveals that the power consumption remains high or increases for a few seconds during a migration instance. This behavior contradicts the aim of power-capping, and may endanger the stability of servers. Based on this observation, we also propose and evaluate two power-suppressing live-migration schemes to resolve the power overshooting issue. Our evaluation shows that both approaches immediately limit the power consumption after live-migration is initiated.