One of the main principles of the current airport slot allocation mechanism in Europe is based on the existence of historical (also called grandfather) rights granted to airlines for using such slots. Through an experimental analysis, we quantitatively show that the system disutility (i.e. the sum of the costs of the individual airlines due to the imbalance between demand and capacity at airports) is higher when grandfather rights (GFRs) are present. Moreover, we consider the interdependence of slots at different airports and we introduce the possibility to fairly redistribute such costs among airlines through monetary compensations. Our results suggest that it is possible to remove GFRs without significantly penalising airlines which own them.