  Bell tests have become a powerful tool for quantifying security, randomness,
entanglement, and many other properties, as well as for investigating
fundamental physical limits. In all these cases, the specific experimental
value of the Bell parameter is important as it leads to a quantitative
conclusion. However, most experimental implementations aiming for high values
of the Bell parameter suffer from the defect of showing signaling. This
signaling can be attributed to systematic errors occurring due to weaknesses in
the experimental designs. Here we point out the importance, for quantitative
applications, to identify and address this problem. We present a set of
experiments with polarization-entangled photons in which we point out common
sources of systematic errors and demonstrate approaches to avoid them. This
allows us to establish a reliable estimate for the Bell parameter.
