The two main reasons why democracy won the contest for the leading legitimacy claim in the modern world are its capacity to generate loyalty and its self-correction potential. In order to use these virtues, the European Commission (conceptualised as the government of the EU) should be elected solely by the European Parliament. According to the general perception, a modification of the treaties would be inevitable in order to achieve such a change. The paper attempts to show that this perception is wrong: there is another (currently more viable) way to achieve this outcome, which was successfully used a long time ago to reform the British constitutional system on a step by step basis. In the U.K., there is currently (and there was) no legal rule prescribing that the monarch has to appoint as Prime Minister the person who commands the majority support of the House of Commons. It is happening though, by a (legally non-binding) constitutional convention. After analysing the concept of constitutional conventions and its applicability to the EU, the paper reaches the conclusion that we can achieve a parliamentary system under the current legal regime, if politicians in the European Parliament have the ambition to take the necessary steps. If it happened, then the EU government system would become similar to some extent to today’s German system, where a party coalition in the lower chamber supports the government, and the upper chamber takes part substantively only in the legislation but not in the formation of the government.