An appliance for drying laundry comprising an appliance cabinet, a laundry treatment chamber inside the cabinet, a drying air recirculation path for causing recirculation of the drying air into/out from the laundry treatment chamber, a drying air propeller driven by a drying air propeller motor ( 240;340f) for causing the drying air to recirculate along the drying air recirculation path, a drying air moisture condensing and heating system ( 205-220,270) located in the drying air recirculation path for dehydrating the moisture-laden drying air leaving the laundry treatment chamber and heating the dehydrated drying air before it re-enters into the laundry treatment chamber, wherein the drying air moisture condensing and heating system comprises a heat pump operating with a refrigerant fluid, the heat pump comprising a refrigerant fluid compressor and a refrigerant fluid expansion device, wherein: - the refrigerant fluid compressor is a variable-output compressor, capable of being driven to work at different compressor working modes, each compressor working mode corresponding to a respective compressor power consumption course and/or compressor rotational speed course and/or frequency course of the supply current/voltage of the compressor, and - the refrigerant fluid expansion device is a variable expansion device, controllable to provide different refrigerant fluid mass-flow rates, wherein the appliance has a user interface comprising a laundry drying cycle selector operable by a user for selecting one out of a number of default laundry drying cycles ( C 1, C 2, C 3,..., C k), and a control unit adapted to control the machine operation, said control the machine operation comprising commanding the compressor to work at a default output corresponding to the selected default laundry drying cycle, controlling the expansion device to provide a default refrigerant fluid mass-flow rate corresponding to the selected default laundry drying cycle, and commanding the drying air propeller motor to work at a default average speed corresponding to the selected default laundry drying cycle, and wherein the user interface comprises a command input means operable by the user for imparting to the appliance a command in response to which the control unit: - commands the compressor to work at a changed compressor output course with respect to the default output; - controls the expansion device to provide a correspondingly changed refrigerant fluid mass-flow rate with respect to the default refrigerant fluid mass-flow rate corresponding to the selected default laundry drying cycle, characterized in that the command input means are operable by the user for imparting to the appliance a command in response to which the control unit commands the drying air propeller motor to work at a changed average speed with respect to the default average speed corresponding to the selected drying cycle. - the refrigerant fluid compressor is a variable-output compressor, capable of being driven to work at different compressor working modes, each compressor working mode corresponding to a respective compressor power consumption course and/or compressor rotational speed course and/or frequency course of the supply current/voltage of the compressor, and - the refrigerant fluid expansion device is a variable expansion device, controllable to provide different refrigerant fluid mass-flow rates, - commands the compressor to work at a changed compressor output course with respect to the default output; - controls the expansion device to provide a correspondingly changed refrigerant fluid mass-flow rate with respect to the default refrigerant fluid mass-flow rate corresponding to the selected default laundry drying cycle,