A car safety supervising unit (SSU) for an elevator having an elevator car displaceable within an elevator shaft includes at least one sensor for sensing car-related parameters and outputting corresponding car-related signals, an I/O interface for inputting input signals into the car SSU and for outputting output signals to external devices and a signal processing unit for processing at least one of the car-related signals and the input signals and for generating the output signals. In an installation operation mode, the signal processing unit processes exclusively the car-related signals and generates the output signals based exclusively on the car-related signals whereby the car SSU accomplishes basic safety functions for safely operating the elevator with a limited number of available sensors. In a normal operation mode, the signal processing unit processes both the car-related signals and the input signals and generates the output signals based on both.