Methods and corresponding systems for determining a transmit power in a wireless device include receiving, in the wireless device, a cell-wide power control parameter related to a target receive power at a serving base station. Thereafter, a transmit power is calculated in response to the cell-wide power control parameter and an implicit mobile-specific power control parameter. The wireless device then transmits using the transmit power. The cell-wide power control parameter can be a cell target signal to interference-plus-noise ratio, or a fractional power control exponent. The implicit mobile-specific power control parameter can be a modulation and coding level previously used by the wireless device, or a downlink SINR level measured by the wireless device.