An Appliance for drying laundry (100) includes a drying-air moisture-condensing system (215,220, 225) comprising a heat pump system with a first heat exchanger (215) for cooling the drying air and a second heat exchanger (220) for re-heating said drying air, and a variable-output compressor (210). At least one Joule-effect heater (255) is located downstream of the heat pump heat exchangers for boosting the heating of the drying air. The appliance can perform at least one drying cycle in: at least a first drying mode, wherein the heater is kept de-energized and the compressor is driven to a first compressor mode having a compressor power consumption course and/or a compressor rotational speed course and/or a frequency course of the supply current/voltage of the compressor motor, and at least a second drying mode, wherein the heater is kept energized for at least an initial portion of the drying cycle and thereafter it is kept de-energized, and the compressor is driven to a second compressor mode comprising a compressor power consumption course and/or a compressor rotational speed course and/or a frequency course of the supply current/voltage of the compressor motor. For at least a portion of the drying cycle after the electric heater has been de-energized, a compressor power consumption and/or a compressor rotational speed and/or a frequency of the supply current/voltage the compressor of the second compressor mode is/are higher than the one/s of the first compressor mode.