Portugal is expected to sell around 2 billion euros of the five-year paper, a reopening of its 4.35 percent October 2017 bond, first launched in 2007 as a 10-year benchmark.
Sources close to the deal said total orders had reached 8 billion euros, allowing guide pricing to be tightened by 10 basis points to mid-swaps plus 400 bps a lower cost of borrowing for Lisbon than initially expected.
"The guidance came down thanks to strong demand. The final yield should settle at around 5 percent or slightly below," one source told Reuters.
Portugal last paid 6.4 percent to sell five-year bonds in a placement before its bailout two years ago. Its outstanding 2017 debt was yielding 4.9 percent in the secondary market on Wednesday, the lowest level since late 2010.
"I think 2 billion euros is a reasonable size that will bolster confidence. That would certainly be a good step towards getting qualified for the ECB programme," said Orlando Green, a debt strategist at Credit Agricole in London.
The European Central Bank's programme of bond purchases, known as Outright Monetary Transactions, is only available to countries that have normal access for long-term bonds and have asked European authorities for help.
The ECB has yet to buy any bonds under the scheme, which was announced in September, although its pledge to support struggling euro zone states has helped drive yields on their debt sharply lower.
"They need the OMT qualification to lower borrowing costs further. They'll still need to issue more debt like this before they get full market access, but then they should fit into the ECB criteria as they are still under bailout," Green said.
Although market sentiment towards the euro zone periphery has become more positive, worries persist about Portugal's economy, tipped into the worst recession since the 1970s by austerity prescribed under the bailout.
That means its window of opportunity in the bond market may be small, warned Ioannis Sokos of BNP Paribas.
"It's a good chance to take advantage of the market momentum, and this may not last forever, as we have elections in Italy coming (in February)", Sokos said.
Neighbouring Spain, still seen as a potential candidate for a bailout, successfully sold a 7 billion euro 10-year bond on Tuesday, while Ireland, whose EU-IMF rescue preceded Portugal's, has already sold bonds ahead of a planned exit from its bailout.
Portugal made its first step towards a market return in October, when it swapped bonds expiring this year for 2015 debt.
Ireland, which returned to debt markets with a similar transaction a year ago and became the first bailed-out country to sell new long-term debt in July, sold another 2.5 billion euros of the same five-year bond this month at a yield of just 3.32 percent.
Its finance minister said on Tuesday he believed Ireland would by able to apply for support from ECB once it has completed two longer-term bond sales.
Also on Tuesday, EU economic affairs chief Olli Rehn said the European Commission was examining ways help Ireland and Portugal return to financing themselves in the bond market as their bailouts come to an end.
"It was very good, helpful timing (for Rehn's comments) that Portugal may benefit from," said Sokos at BNP Paribas.
Under its aid programme, Lisbon is financed until late 2013, after which it will need to maintain access to bond markets.
Portuguese 10-year yields, which were around 18 percent a year ago, settled below 6 percent on Tuesday for the first time since late 2010 and fell further to 5.81 percent on Wednesday.