A rotary compressor 1 comprises a cylindrical housing 8, a cylindrical roller 10 accommodated in the housing 8, a motor shaft 13 leading through the roller 10 having a cam 14 for rolling the roller 10 along a side wall 15 of the housing 8, and a discharge port 18 leading through a bottom cover 12, wherein a height-to-radius ratio hr/rr of the roller 10 is between 1.6 and 1.2, a radius rs of the motor shaft 13 is 8.0 mm or less, a cam height hc of 14 mm or less, an area Q of the discharge port 18 of 17 mm 2 or more, and a thickness d of the discharge port 18 of 2.5 mm or less. For operation of the compressor 1, a top cover 19 may be put onto the top open side of the housing 8. The top cover 19 may have a bushing for the shaft 13. A heat pump P comprises the compressor 1. A household appliance H, in particular laundry care apparatus H, comprises the heat pump P.