Dealing with the connection between banks and government debt — a toxic loop that has forced several countries to ask for bailouts after they tried to rescue their banks — also addresses a major cause of the region's financial crisis.
"The crisis came by way of the banks and now a tool is in place so that nothing will be like it was before," declared French President Francois Hollande on his way into Thursday's summit.
However, serious challenges remain: The economy across the eurozone is in recession; unemployment is rising; and in recent days, industrial production and retail sales have fallen further than forecast.
And while leaders have reached a couple of significant agreements this week, there are still some tough problems to crack.
In its attempts to strengthen the Europe against future financial crises, the EU has made significant promises about the kinds of powers it's ready to hand over to the central bureaucracy. On Thursday, leaders discussed the possibility of having their countries enter into individual contracts with the EU to ensure they keep their commitments to cut excessive spending and adopt important reforms to make their economies more competitive.
They also talked about creating a budget for the eurozone that could help prop up countries that are struggling under the weight of reforms — as Spain and Greece are now.
The problem leaders face is that they are concentrating so much power in Brussels that they need to make institutions and leaders who are now largely unknown accountable to voters. Some countries that don't use the euro are also beginning to worry about being marginalized in the EU as the countries that do use the currency build up their institutions.
Nonetheless, Hollande said the work of the past days allowed for "a good conclusion to 2012."
"That is, both to fix the problems of the past and to open a new possibility to a deeper economic and monetary union."
Raf Casert, Sylvie Corbet and Robert Wielaard in Brussels, Geir Moulson in Berlin and Elena Becatoros in Athens contributed to this story.