Yesterday, the 17 eurozone finance ministers agreed on how the single currency's rescue fund, the European Stability Mechanism, could help the banks without adding to the already big debt burden on member states.
The next step is to decide how to close down banks when that is the best solution, with the two facets combined in a Banking Recovery and Resolution Directive.
"We have a fair chance of concluding the work, it is very important in maintaining momentum on the banking union," EU Economic Affairs Commissioner Olli Rehn said today.
Negotiations on the resolution mechanism look like being difficult as it goes to the heart of who has ultimate control over a country's banks.
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Some states, for example Britain among the non-eurozone countries, are notably cautious on ceding more authority to Brussels given its jealously guarded financial centre in the City of London.
"We have made significant progress in narrowing the ground (but) ... There are still some significant divergences of opinion," Irish Finance Minister Michael Noonan said as he went into the talks.
Another key problem is who foots the bill, with bank creditors, including large depositors, now ranked to be 'bailed-in' and forced to make a contribution.
Some countries fear that a bail-in could so weaken a creditor that it has an unintended knock-on effect on other companies, proving counter-productive in the end.
Ministers and analysts welcomed yesterday's eurozone ESM deal as a major step towards "banking union," the new EU regulatory framework meant to contain any bank collapse.
"The essence of this measure is to dilute the link between banks and governments which is positive," Diron said.
"The restructuring of the banking system has been delayed for too long which is one of the reasons why the eurozone cannot grow out this recession," she added.