Euro Zone finance ministers hunted Monday for possible compromises on a new scheme to shield taxpayers from bank bailouts, as three days of last—ditch negotiations on the measure got under way.

The mechanism to wind down troubled Euro Zone banks would be the second element of a crisis-thwarting banking union, considered key to restoring trust in the currency bloc.

The 18 ministers had been expected to put the finishing touches Monday to an intergovernmental agreement to steer a new fund from which troubled banks could get assistance.

The chair of their Euro Group panel, Dutch Finance Minister Jeroen Dijsselbloem, said “very good progress” had been made, but that some issues remain to be finalised on Tuesday, when ministers from the wider, 27-country European Union will meet.

The EU ministers are trying to hammer out a compromise with the bloc’s parliament before European elections in May. Diplomats say they believe that a decision would otherwise be delayed until 2015, potentially to the detriment of EU credibility.

The last chance for European Parliament to endorse any deal is at its April 14-17 session.

The legislature, which must approve the aspects of the wind-down scheme not related to the fund, is unhappy with the ministers’ approach and has threatened to block the whole scheme.

The legislature resents the intergovernmental agreement because it prevents parliament from having a say in the fund. It has concerns about decision-making processes in the overall scheme, which it argues are too complicated to quickly save a troubled bank.

To placate lawmakers, the ministers are considering a concession on the time foreseen to build up the new fund, shortening it from the 10 years previously planned. They may allow the fund to borrow from financial markets, in a bid to make it more credible.

The next round of negotiations with parliament will be Wednesday, but its representatives were already involved in the Euro Zone talks on Monday evening.

Earlier, the ministers reviewed progress in Greece, which has been tied up in negotiations with its international creditors since September to figure out its next economic steps.

The lack of an agreement is preventing the disbursement of bailout money earmarked for the country. Greece needs access to the aid by mid-May, when it faces a large bond redemption.

Dijsselbloem expressed optimism that Athens will finally strike a deal with experts from the European Commission, European Central Bank and International Monetary Fund (IMF) by the end of this week.

Also Monday, ministers received details about financial aid the EU intends to offer crisis—ridden Ukraine.

“Ukraine lies in the middle of the European continent. We need to do our part to ensure stability and security in that important part of Europe,” EU Economy Commissioner Olli Rehn told journalists. “It is essential to create conditions for economic stabilization.” He noted that EU assistance depends on Ukraine and the IMF putting in place a support agreement, and Kiev starting to pursue “serious economic reforms.”