That was the key part of talks between Greece and private bondholders on a debt swap on Tuesday, which made progress but ended without agreement.
It could see private sector creditors rank "pari passu" with the claims of the EFSF euro zone bailout fund and sovereign creditors, with coupons on the new bonds paid to banks and other investors at the same time as interest payment on loans.
"We've made progress, but there are a number of remaining unresolved issues that will require much further effort by all parties if we're to find common ground," Charles Dallara, head of the Institute of International Finance (IIF), told Reuters by telephone.
Talks were likely to restart in Paris on Thursday or Friday, he said.
The two sides are still haggling over the coupon rate and sweeteners to seal a deal, bankers involved in the discussions said.
The bond swap, dubbed private sector involvement (PSI+), is a key part of the debt-choked country's 130 billion euro ($170 billion) bailout, and Athens is keen to clinch a deal by the end of January to secure crucial budget relief before elections due on February 19.
As the private sector and government try to bridge a gulf between the two sides, bankers involved in the talks said they found some common ground with the co-financing structure, which would improve the quality of the new Greek bonds issued to banks.
"Banks moved towards the sovereigns' proposal on the condition that the new bonds have about the same credit status as official sector loans," a banker involved told Reuters.
Dallara said the private sector and Greek authorities "had a sense of urgency" after previous talks had stalled.
"It's very clear that it's vital for Greece and Europe that we find common ground on a voluntary deal, so that's why all parties need to show some willingness to compromise," he said.
At a summit on October 27, euro zone leaders reached a deal with private banks and insurers to accept a 50 percent loss on the notional value of outstanding Greek bonds they hold in exchange for new instruments.
The writedown is designed to help cut Greece's debt ratio to 120 percent of GDP by 2020 from 160 percent this year. It will also save the state 5.1 billion euros in interest payments next year.
But negotiations on the details of the voluntary restructuring of 206 billion euros of outstanding Greek government paper in private sector hands face sticking points.
They include the coupon rate on the bonds and the assumed discount rate, which determine the loss banks will incur in terms of net present value (NPV). NPV is a measure of the current worth of the bonds' future cash flows.
A successfully concluded debt swap is key to meeting Greece's target to cut its budget gap to 5.4 percent of GDP next year from a target of 9 percent this year and attain a primary surplus.
The International Monetary Fund's mission chief for Greece Poul Thomsen said on Tuesday he was optimistic that a deal with private-sector bondholders would be reached early next year, but he declined to discuss specifics.
"I think the PSI is key to securing debt sustainability, and of course to ensure adequate financing for the program for the next 12 months," he told reporters in a conference call.
"I am confident that we will get this PSI, reducing debt to 120 percent of GDP" by 2020, he added.
Failure to reach an agreement on a voluntary writedown of the bonds would have huge ramifications for Greece and the insurance policies written on its debt, known as credit default swaps.
Sources have previously told Reuters that Greece is offering bondholders 15 euros in cash and new bonds with a face value of 35 euros, paying a coupon of around 4.5 percent for every 100 euros of outstanding bonds.
But private creditors want the new bonds to pay a higher coupon of 8 percent, with principal backed by AAA-rated assets.
Athens is being advised by law firm Cleary Gottlieb Steen & Hamilton on implementing the debt swap, with Lazard Freres acting as its financial adviser. ($1 = 0.7641 euros)