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 the drying air through the drum , a motor adapted to drive the drying air fan , 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 , and a laundry load indicating or detecting unit adapted to determine or estimate the amount of laundry in the drum, wherein the compressor is a variable speed and/or variable power compressor; and wherein the method comprises: starting (S6) a drying program for drying the laundry received in the drum , operating (S8c, S10) the compressor at an initial compressor output, determining or estimating (S8b, S12) the amount of laundry in the drum at least once during the drying program, characterized in that the method further comprises: setting (S14) a threshold value (TH1) for an operation parameter (P) of the heat pump system in dependency of the determined or estimated amount of laundry, monitoring the operation parameter (P) of the heat pump system of the laundry drying apparatus , and operating (S20) the compressor at a reduced compressor output if the monitored operation parameter (P) reaches or exceeds the set threshold value (TH1). a drum adapted to receive laundry for drying the laundry using drying air, a drying air fan adapted to convey the drying air through the drum , a motor adapted to drive the drying air fan , 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 , and a laundry load indicating or detecting unit adapted to determine or estimate the amount of laundry in the drum, wherein the compressor is a variable speed and/or variable power compressor; and starting (S6) a drying program for drying the laundry received in the drum , operating (S8c, S10) the compressor at an initial compressor output, determining or estimating (S8b, S12) the amount of laundry in the drum at least once during the drying program, characterized in that the method further comprises: setting (S14) a threshold value (TH1) for an operation parameter (P) of the heat pump system in dependency of the determined or estimated amount of laundry, monitoring the operation parameter (P) of the heat pump system of the laundry drying apparatus , and operating (S20) the compressor at a reduced compressor output if the monitored operation parameter (P) reaches or exceeds the set threshold value (TH1). setting (S14) a threshold value (TH1) for an operation parameter (P) of the heat pump system in dependency of the determined or estimated amount of laundry, monitoring the operation parameter (P) of the heat pump system of the laundry drying apparatus , and operating (S20) the compressor at a reduced compressor output if the monitored operation parameter (P) reaches or exceeds the set threshold value (TH1). <EOS>