What a difference a dollar makes. The offer of dollar funding by the European Central Bank and other global central banks to ward off a liquidity crisis among eurozone banks prompted a relief rally in their shares on Thursday. The combined action of the ECB, Federal Reserve, Bank of England, Bank of Japan and Swiss National Bank also prompted a surge in the euro against the dollar, pound and yen.

The central banks’ three-month liquidity injections (in addition to existing ECB weekly funding) will tide over eurozone banks unable to raise dollars from US lenders through the year-end. But the healing balm will bring only fleeting relief. It will not cure the underlying malaise of decision paralysis that afflicts the eurozone’s policymakers.

The eurozone crisis has wreaked untold damage on the bloc’s banking sector. Italian and French bank shares have been battered, and eurozone banks’ traditional dollar funding sources dried up on concerns about their exposure to the debt of peripheral European sovereigns, especially Greece. BNP Paribas and Société Générale this week rolled out plans to bolster their capital positions, despite signs that they could withstand a Greek writedown. The bigger fear of traditional funding providers, given eurozone banks’ exposure to government debt, is contagion, however. Governments have less flexibility to support troubled banks post-crisis.