The paper deals with the definition of eligibility criteria for regions and states to draw resources within the Convergence objective and the Regional Competitiveness and Employment objective of the EU Cohesion Policy funds. It proposes which regions and countries should be regarded as poor ones and to what extent they should be eligible for financing. The paper proposes that support would only go to regions in Member States poorer than the EU average and, within these countries, support would only be available to NUTS 2 regions poorer than the EU average. In addition, the difference between the region's GDP per capita in PPS and the EU average would be reflected by setting a ceiling for maximum admissible allocation to eligible regions between 1 and 4% of the region's GDP in EUR. The paper also proposes to abolish the Cohesion Fund. Finally, eligible regions and countries are identified based on a numerical model, where support going to regions with lower-than-average GDPpc PPS belonging to countries with lower-than-average GNIpc PPS is also calculated.