Method for operating a laundry drying apparatus, in particular a laundry dryer or a washer-dryer, during a drying program, the laundry drying apparatus comprising: a drum adapted to receive laundry for drying the laundry using drying air, a drying air fan adapted to convey drying air through the drum, a motor adapted to drive the drying air fan, and a heat-pump system comprising a first heat exchanger adapted to heat the drying air, a second heat exchanger adapted to cool the drying air for humidity condensation, and a compressor adapted to circulate refrigerant through the first and second heat exchangers (10, 12), wherein the compressor is a variable speed and/or variable power compressor; wherein the method comprises: starting a drying program for drying the laundry received in the drum, during a first phase of the drying program, operating the compressor at a first compressor performance and operating the drying air fan at a first fan performance, and during a second phase of the drying program, operating the compressor at a second compressor performance and operating the drying air fan at a second fan performance, wherein the second compressor performance is lower than the first compressor performance, and wherein the second fan performance is higher than the first fan performance, wherein the compressor performance is one or more of: a motor speed of a motor driving the compressor, an electrical power supplied to the compressor, the frequency of the voltage and/or current applied to the motor of the compressor, and the refrigerant conveyance rate of the compressor; wherein the drying air fan performance is one or more of: a motor speed of the motor driving the drying air fan, and the air conveyance rate of the drying air conveyed by the fan; and wherein one or more of the following applies: the change from first to second phase, the triggering event for changing from the first to the second phase, or the ending of the first phase and the starting of the second phase is controlled or is defined by a compressor cooling phase where for the first time a compressor cooling fan is started or activated the first time for cooling the compressor, at the start of the second phase a compressor cooling fan is activated for cooling the compressor, and during the second phase a compressor cooling fan is at least repeatedly operated or activated for cooling the compressor. a drum adapted to receive laundry for drying the laundry using drying air, a drying air fan adapted to convey drying air through the drum, a motor adapted to drive the drying air fan, and a heat-pump system comprising a first heat exchanger adapted to heat the drying air, a second heat exchanger adapted to cool the drying air for humidity condensation, and a compressor adapted to circulate refrigerant through the first and second heat exchangers (10, 12), wherein the compressor is a variable speed and/or variable power compressor; starting a drying program for drying the laundry received in the drum, during a first phase of the drying program, operating the compressor at a first compressor performance and operating the drying air fan at a first fan performance, and during a second phase of the drying program, operating the compressor at a second compressor performance and operating the drying air fan at a second fan performance, wherein the second compressor performance is lower than the first compressor performance, and wherein the second fan performance is higher than the first fan performance, wherein the compressor performance is one or more of: a motor speed of a motor driving the compressor, an electrical power supplied to the compressor, the frequency of the voltage and/or current applied to the motor of the compressor, and the refrigerant conveyance rate of the compressor; a motor speed of a motor driving the compressor, an electrical power supplied to the compressor, the frequency of the voltage and/or current applied to the motor of the compressor, and the refrigerant conveyance rate of the compressor; wherein the drying air fan performance is one or more of: a motor speed of the motor driving the drying air fan, and the air conveyance rate of the drying air conveyed by the fan; and a motor speed of the motor driving the drying air fan, and the air conveyance rate of the drying air conveyed by the fan; and wherein one or more of the following applies: the change from first to second phase, the triggering event for changing from the first to the second phase, or the ending of the first phase and the starting of the second phase is controlled or is defined by a compressor cooling phase where for the first time a compressor cooling fan is started or activated the first time for cooling the compressor, at the start of the second phase a compressor cooling fan is activated for cooling the compressor, and during the second phase a compressor cooling fan is at least repeatedly operated or activated for cooling the compressor. the change from first to second phase, the triggering event for changing from the first to the second phase, or the ending of the first phase and the starting of the second phase is controlled or is defined by a compressor cooling phase where for the first time a compressor cooling fan is started or activated the first time for cooling the compressor, at the start of the second phase a compressor cooling fan is activated for cooling the compressor, and during the second phase a compressor cooling fan is at least repeatedly operated or activated for cooling the compressor.