Inter-TSO payment methods (ITC methods) provide the aggregate compensations and charges faced by countries in a region, because of the use that agents in each country make of the transmission grids of the other countries. These compensations and charges should modify local access charges in each country. The paper closely examines the most promising methods for computing ITCs presently considered in the Internal Electricity Market (IEM) of the European Union, namely the Average Participations (AP) method and the With and Without Transits (WWT) method. Some attention is also given to a third method that lies somewhere between the two previous ones: the Average Participations applied to Transits (APT) method. The performance of the AP, WWT and APT methods is compared with that of the temporary method presently applied to compute compensations in the IEM. The three methods are closely examined both from a conceptual point of view and taking into account the numerical results they produce. Based on this analysis, the AP method is proposed as the best option to compute ITCs in the European Union. The paper draws on research projects carried out for the European Commission and the Florence Regulatory Forum. (c) 2006 Elsevier Ltd. All rights reserved.