Encouraging as the agreement was to advocates of an alternative European power, there were very specific reasons both for the unity displayed and for the success of its purpose. And recent history has demonstrated that the three EU heavyweights are still fundamentally divided on how to approach other key issues - notably the transatlantic alliance.
Although France and Germany have enjoyed historically close relations since their united front over Iraq, they continue to have distinct foreign policy goals. Both are strong supporters of broader issues such as the need to make major international decisions strictly through the UN and the importance of a common European defence force. But on some specifics of foreign policy, there are areas of potential disagreement.
The ministers made it very clear when they were in Tehran that they represented only their own nations; not the EU and not other bodies. However, Jack Straw said he believed the move also reflected the wishes of their allies. He could not have made himself understood more clearly: London and Washington had closely discussed the European deal and the US had said it was in favour. It is difficult to imagine that London - during this period in its relations with Washington - would actually go against its wishes.
US criticism of Europe's policy of engagement with Iran has been more muted of late as European countries added to the international pressure on Iran's nuclear programme. In Iran, this was seen as a change in policy to please Washington. There seemed to be little understanding that Europe was seriously concerned in its own right about Iran's nuclear transparency.
Engagement was also suffering for other reasons. European diplomats felt that Iran had repaid little of the trust it had been given. Except for some developments in human rights, there had been little co-operation in other matters of international concern. And over the past two years, it has become evident that President Mohammed Khatami's reformist movement holds limited political power and is on the back foot.
For all that, the deal suited everybody. Europe's faith in engagement appears to hold good. The US can stand back and enjoy the fruits of the agreement but put the pressure back on if Iran fails to deliver.
Most of all, this was a success for international diplomacy, which is being pieced back together after the shattering effects of the Iraq crisis. And more specifically, the agreement represented a success for the policy of engagement over aggression.
From the other side, Iran's clerical leaders have demonstrated they will respond - eventually - to a good deal if it is backed up by some pretty juicy threats. They may also have learned - as the reformist press has been at pains to point out - that it is better to make the deal early. Had Iran responded to the European offer when it was first made in the summer, it would only have had to sign the additional protocol. Uranium enrichment was then not even under discussion.