A transmitter comprises a power amplifier (PA) which has an amplifier powersupply input (PI) and an output (PAO) to supply a transmission signal (Vo) with an output power (Po). A power supply (PS) has power supply outputs (PSO1, PSO2) to supply a first power supply voltage (PV1) and a second power supply voltage (PV2). A switching circuit(SC) is arranged between the power supply outputs (PSO 1, PSO2) and the amplifier powersupply input (PI). A controller (CO) has an input to receive a power change command (PC) to control: first (i) the switching circuit (SC) to supply the first power supply voltage (PV1) to the amplifier power-supply input (PI), and the power supply (PS) to vary a level of the second power supply voltage (PV2), the level of the second power supply voltage (PV2) being lower or higher than a level of the first power supply voltage(PV1) if the power change command (PC) indicates that the output power has to decrease or increase, respectively, and secondly (ii) the switching circuit (SC) to supply the second power supply voltage (PV2) to the amplifier power-supply input (PI).