The most commonly used performance indicator (PI) of heat pump (HP) systems is the COP. But is it a good PI? If so, does it have a minimum threshold? This article covers the potentials and constraints of different PIs for HP systems implemented in non-renovated residential buildings from an environmental, economic and social acceptability point of view, based on real case studies situated in Geneva, Switzerland. After describing the Geneva context and listing the most common PIs, we first compare a traditional gas boiler to an air to water HP system for space heating and domestic hot water of single-family building (SFB). We then follow by a similar comparison for multifamily buildings (MFB). For this particular building demand, a hybrid system is also analyzed (HP combined with gas for the peak loads) and specific PIs are included. Finally, the most pertinent PIs for air to water HP systems are identified and the minimum COP value of 2.5 is recommended to insure the reliability of the system in the 3 mentioned fields in the swiss context.