The cumbersome coppers have only been in circulation for three years, along with higher value euro notes and coins. But now Belgium and the Netherlands are set to follow Finland and round bills to the nearest five cents ($0.06).
Other eurozone countries are warier, with Germany concerned a similar move would reignite inflation angst amongst its penny-pinching shoppers.
One and two cent coins will remain legal tender throughout the eurozone, but those countries rounding bills want to reduce the sheer volume of coins in circulation.
"Shopkeepers hope they can settle bills faster," Dutch central bank spokesman Tobias Oudejans said. "In the retail sector, long queues are one of the most expensive points. To help more shoppers in less time with fewer tills will save them a lot of hassle."
The Netherlands is set to start paying to the nearest five cents as of Wednesday, following Finland which has been doing this since euro notes and coins were introduced at the start of 2002. Belgium is likely to follow suit.
Brussels grocery store owner Isabelle Silva would be happy to see small change go. "The coins are really annoying. No one has any time for small change."
Sandwich store manager Claudine Devallejo shared her sentiment, as she flung open a cash register brimming with small change. "You can't easily reuse the coins, as when you give them in change, people are never happy."
Although shops return their spare change to the bank, consumers often hoard theirs, forcing countries to mint millions of extra coins at a cost greater than face value.
"That's a cost for the treasury," said Serge Bertholome, a Belgian central bank official in charge of a task force looking at the future of the coins in the country.
Belgium's Royal Mint expects to produce 200 million one and two cent coins next year, at a cost of several million euros.
Add to that the approximate one-million-euro annual handling cost Belgian banks believe they face and the time retailers spend sorting the coins, and the problem becomes clear - Dutch retailers estimate the coins cost them 30 million euros a year.
According to a European Union survey, most Dutch and Belgians want to scrap the one and two cent coins.
Bertholome said the Belgian central bank had brokered an agreement among banks, retailers and consumer groups to round bills to the nearest five cents.
But the change is unlikely to come into force before 2005 due to technical issues and the need for new legislation.
Not everyone is looking forward to a change, though.
"I think it will make things much more expensive," said Brussels newsstand owner Erik Scheers. "Already some things have grown really overpriced as a result of introducing the euro."
In theory, the impact of rounding prices on inflation should be zero, as shops are obliged to round bills to the nearest five cents and not automatically upwards.
A customer would pay 1.35 euros for a 1.37-euro bill, for example. Prices tags are not rounded - only the final bill.
Based on Finland's experience, Belgium's central bank expects prices to rise by no more than 0.1 percentage points.
Even in a worst-case scenario in which retailers raise all marked prices to the nearest five cents, inflation would be only expected to rise 0.4 percentage points at the most.
"If prices are rounded up, that could lead to some inflation in small items in the retail sector," Fortis Bank economist Elwin de Groot said. "But we shouldn't exaggerate it. Small items only make up a small part of consumer spending."
But perception can be more damaging than reality.
The introduction of euro notes and coins in 2002 caused at most marginal increases in inflation overall, yet price rises for some everyday items jaundiced Europeans' attitudes.
As a result, German retailers are emphatic that they do not want the eurozone's largest member to phase out the coins.
"Any type of rounding could unsettle consumers. We cannot afford that in the current economic situation," Hubertus Pellengahr, a spokesman for Germany's largest retail organisation HDE, said recently.
Belgian central banker Bertholome regrets his country did not join Finland in eschewing the one and two cent coins from the beginning.
"I think it was perhaps a missed opportunity, but at that time there was so much concern about inflation," he said. "Perhaps people did not see the inconvenience of small coins. Now they do."