A radio communication system has means for improving power control of a communication channel for the transmission of data after an interruption in the transmission. This is done by adjusting the transmission power immediately after the interruption by an offset from the power used before the interruption. The offset may be fixed or may be determined from the transmission power in the period before the interruption. This technique reduces, on average, the time taken for power control to be re-established, thereby addressing the problem that data transmissions immediately after the interruption are likely to be corrupted if the power level is too low, or to generate extra interference if the power level is too high.