The covariance of ground-based lucky images is a robust and easy-to-use algorithm that allows us to detect faint companions surrounding a host star. In this paper, we analyse the relevance of the number of processed frames, the frames' quality, the atmosphere conditions and the detection noise on the companion detectability. This analysis has been carried out using both experimental and computer-simulated imaging data. Although the technique allows us the detection of faint companions, the camera detection noise and the use of a limited number of frames reduce the minimum detectable companion intensity to around 1000 times fainter than that of the host star when placed at an angular distance corresponding to the few first Airy rings. The reachable contrast could be even larger when detecting companions with the assistance of an adaptive optics system.