  In this report we provide an improvement of the significance adjustment from
the FA*IR algorithm of Zehlike et al., which did not work for very short
rankings in combination with a low minimum proportion $p$ for the protected
group. We show how the minimum number of protected candidates per ranking
position can be calculated exactly and provide a mapping from the continuous
space of significance levels ($\alpha$) to a discrete space of tables, which
allows us to find $\alpha_c$ using a binary search heuristic.
