Market evidences of the last three years show that the application of the Emission Trading Scheme (ETS) may endanger the European electricity intensive industries both directly and indirectly. The direct ETS burdens come from the costs of both abating emissions from old technologies and buying emission allowances on the market. The pass through of carbon cost in electricity price implies an indirect ETS charge. The combined action of these two carbon burdens may negatively affect European industries' competitiveness at international level. Some of these industries are threatening to relocate their production activities outside of Europe. This would lead to the so-called "carbon leakage" phenomenon. Taking stock of a French industrial proposal, I consider some special contractual policies whereby electricity intensive industries can buy electricity at average cost. The rest of the market is instead priced at marginal cost. Thanks to these contracts, generators reserve part of their power plants for these industries and apply to them a price depending on the average capacity, fuel and emission costs of these dedicated units. In addition, these contracts account for the average transmission charges. Industries can choose to be supplied either at a single regional average cost price or at zonal (assimilated to nodal) average cost prices (in which case transmission costs are equal to zero). The final objective consists in analyzing the effects provoked by the application of the single and the nodal average cost prices in the cases where generators dispose of fixed capacity or can invest in new technologies. The market for transmission services is of the "flow based market coupling" type and the allowance price is endogenous. The results show that power contracts indeed partially relieve the direct and the indirect carbon costs and mitigate the incentive of European electricity intensive industries to relocate their activities, but with quite diverse regional impacts in correspondence with different national power policies. Finally, the EU-ETS drives generators' investment choices towards clean and nuclear based technologies. Models are formulated as non-monotone complementarity problems with endogenous electricity, transmission and allowance prices. These are implemented in GAMS and solved by PATH. They are applied to a prototype power system calibrated on four countries of the Central Western Europe represented by France, Germany, Belgium and The Netherlands.