Rehabilitating Greek banks poses a difficult question. Should the eurozone take a stake in the lenders, first requiring bondholders and even big depositors to shoulder a loss, or should the bill for fixing the banks instead be added to Greece's debt mountain?
Answering this could hold up agreement on a third bailout deal for Greece that negotiators want to conclude within weeks.
The longer it takes, the more critical the banks' condition becomes as a €420 ($460) weekly limit on cash withdrawals chokes the economy and borrowers' ability to repay loans.
"The banks are in deep freeze but the economy is getting weaker," said one official, pointing to a steady rise in loans that are not being repaid.
This cash 'freeze' is unlikely to thaw soon, although capital controls may be slightly softened, such as the loosening on Friday of restrictions on foreign transfers by businesses.
"Ultimately, you can only lift the capital controls when the banks are sufficiently capitalized," said Jens Weidmann, the head of Germany's Bundesbank, which pushed the ECB to pare back bank funding, leading to their three-week closure.
The debate is interlinked with a wrangle over reforms, about Greek sovereignty in the face of European controls and whether the country can recover with ever rising debts that have topped €300 billion, far bigger than its economy.
Were another €25 billion to be piled on top - the amount foreseen for the recapitalization of Greek lenders - it would add to debts that the International Monetary Fund has argued are excessive.
Greek officials, alarmed by a downward spiral in the economy, want an urgent release of funds for their banks.
Four big banks dominate Greece. Of those, National Bank of Greece, Eurobank and Piraeus fell short in an ECB health check last year, when their restructuring plans were not taken into account. The situation is now dramatically worse.
With its economy starved of cash and the threat of its departure from the eurozone hanging over talks, Athens' room for maneuver is limited. One eurozone official summarized the mood: "Whatever sympathy there was for Greece has evaporated."