nRF51822 power consumption when BLE advertising/connected

We're trying to decide at what voltage we should run our nRF51822 on the next revision of our board. To date we've been doing fine at 1.8V. The current drawn on a 3.7V lithium ion battery while in a connected state for BLE is 0.8mA at the moment.

All other things being equal, we would now prefer to run the Nordic at 3.0V because we have other modules on the board running at 3.0V and we want to use the UART with them without doing any level shifting on the UART lines.

My question is: by raising the voltage at which we're running the Nordic, are we also raising the power consumption when in a BLE connected state? Or is the power consumption constant so by raising the voltage we're lowering the current drawn to arrive at the same power consumption?