In late October, six primary dealer banks used a so-called "swap box," facilitated by Brussels-based settlement house Euroclear. The next round is due to take place on Wednesday.
The box matches short positions with long ones in a bid to make the unwinding of hedging as orderly as possible.
"(Clients can) swap the short against the long (positions) which can allow them to close out a portion of these short positions, while leaving everyone with the same net exposure as before," said Euroclear director Ivan Nicora.
Only securities of a similar economic value can be exchanged, Nicora said.
The move shows that markets are preparing for the much-vaunted plan to rescue Greece from a vicious cycle of weak economic growth and massive payments on its debt -- this despite talk that the deal hammered out between governments and banks may be on the rocks.
Under the plan, banks will have their existing bonds replaced by new paper, taking a 50 percent loss on face value in the process.
The participants in the swap box scheme are primary dealers, those with exclusive rights to buy bonds from the government upon issuance, and are usually also market makers.
As holders of bonds by necessity, market makers aim to keep their own positions flat by taking out balancing short positions.
To create a balancing short position, a holder of a security borrows another one from a different holder, and then sells it.
Any loss caused by a fall in value is then recovered when the borrowed security is repurchased at a lower price and returned to the lender.
But in a case like this one, where the instrument borrowed is no longer available in the market, lenders of the security can request punitive rates.
There are 22 primary dealers in Greek sovereign debt, including UBS, Societe Generale, Royal Bank of Scotland, Nomura, Morgan Stanley, ING Bank and BNP Paribas.
The dealers are represented by the Association for Financial Markets in Europe (AFME), which had asked Euroclear to set up the swap box.
"There is no change of overall net exposure, (there is) just a reduction in the level of shorts to the extent we find pairs of shorts and longs," said Nicora.
"The ability of the swap box to reduce the shorts depends very much on whether we can find pairs on a multilateral basis (between participants)," he said.
Dealers swapped 33 million euros ($45 million) in the first run, and at least a similar amount was expected this week. A final call on whether the second run would take place would be made late on Tuesday.
The swap may have improved liquidity in the largely frozen market for Greek sovereign debt and triggered banks to swap further short positions bilaterally, Euroclear said.
($1 = 0.727 Euros)