Integrated circuits are provided that have volatile memory elements. The memory elements produce output signals. The integrated circuits may be programmable logic device integrated circuits containing programmable core logic including transistors with gates. The core logic is powered using a core logic power supply level defined by a core logic positive power supply voltage and a core logic ground voltage. When loaded with configuration data, the memory elements produce output signals that are applied to the gates of the transistors in the core logic to customize the programmable logic device. The memory elements are powered with a memory element power supply level defined by a memory element positive power supply voltage and a memory element ground power supply voltage. The memory element power supply level is elevated with respect to the core logic power supply level.