We derive the exact finite sample distribution of the L1-version of the Fisz-Cramér-von Mises test statistic (L1-FCvM). We first characterize the set of all distinct sample p-p plots for two balanced sample of size absent ties. Next, we order this set according to the corresponding value of L1-FCvM. Finally, we link these values to the probabilities that the underlying p-p plots emerge. Compa...