By Nick Childs
BBC World Affairs correspondent
The Bulgarian parliament has endorsed the decision to pull the country's 450 troops out of Iraq by the end of the year.
Bulgarian troops have been in Iraq since 2003
Japan is reported to be planning to do the same thing.
The Ukrainians, among others, have been withdrawing. Poland is cutting its commitment.
After some very acrimonious departures in the past - like that of the Philippines - it is difficult to escape the impression that Washington's band of coalition partners in Iraq is dwindling.
Of course, US officials would prefer it was not happening, with the security situation still very uncertain.
One bit of good news for the Americans has been that, despite recent strains in their relations, Italy seems to be staying for now.
But the departures probably will cause some headaches as US commanders of the multinational force in Iraq try to plug emerging gaps.
That the insurgency remains potent and deadly is not in doubt, and the recent upsurge in attacks is a reminder of the underlying capabilities of the insurgent groups and of how difficult countering an insurgency is.
Two Bulgarian soldiers were buried even as the pullout was confirmed
Even so, the trend in departures is probably less troubling now for Washington than it would have been one year ago.
That is partly because the emphasis of the US-led security effort in Iraq has been changing.
The emphasis on coalition offensive military operations has given ground to a lower-profile training role, with ever more emphasis on training and equipping Iraqis to fulfil the security role.
One thing the resilience of the insurgency has prompted is that US defence officials are now saying in public what many have for a long time been saying in private.
The Americans now admit that they will not defeat the insurgency, but that it will be up to the Iraqis themselves, that it will take years to do it, and that it will need a combination of security, political, and economic means - not just military might.
Weight of commitment
Clearly Iraqi forces are not really up to the job yet.
And the focus of insurgent attacks on the Iraqi forces is surely posing problems for Washington in meeting its goals. Still, US defence officials put the number of Iraqi forces now trained and equipped at over 160,000.
At least 18 Ukrainians have now died serving in Iraq
Of course, all coalition partners, even the United States, have found the stresses and strains of their military commitments in Iraq difficult to avoid.
Even the US military is groaning under the weight of its Iraq commitment.
Few participating governments can have expected that the mission in Iraq was going to be as protracted and costly as it has proved to be.
Many made their commitments in the face of domestic opposition.
Many imposed very tight restrictions on just how and where their troops could be used, which posed their own problems for US commanders.
In some ways it's not surprising the coalition is fraying somewhat.