The manner of their release, a signing ceremony attended by the Rev Jesse Jackson and a Yugoslav brigadier-general in front of jostling American news cameramen at the Yugoslav Army Press Office, clearly indicated that President Slobodan Milosevic was seeking to overcome the effects of weeks of demonisation in the press of most Nato countries, and was perhaps seeking to start serious negotiations.
Mr Jackson, who reportedly induced the Yugoslav president to join him in prayer in spite of his well-documented dislike of religion, is travelling back to the United States with a personal letter from Mr Milosevic to President Bill Clinton. Little is known of its contents except that the Yugoslav leader apparently expresses his desire for a face-to-face meeting and offers details of his latest position on the nature of a possible multinational peace-keeping force in Kosovo.
Earlier, the Yugoslav Leftist Party (JUL) said Yugoslavia could accept an international force under the United Nations flag in Kosovo.
Government sources are suggesting that, along with a large Russian contingent, this might include soldiers from some Nato states such as Greece and Italy, though not from what are seen as the "principal aggressor" nations, the United States and Britain.
JUL - whose slogan is "JUL is cool" - is controlled by President Milosevic's wife, Mira Markovic, who is seen by many as the power behind the throne.
The offer falls well short of Nato's demand for a force with an alliance core.
It is still not clear whether it was the increasingly beleaguered Yugoslav leader or the wily, media-conscious American preacher who made the better deal over the release of the prisoners. Mr Milosevic will be gratified by Mr Jackson's call for a halt to the bombing and negotiations, as well as the hope he expressed at the Croatian border that "the Nato alliance will see this for what it is and not be cynical".
But if Mr Milosevic has learnt anything of American television politics it must be that such statements have an extraordinarily brief shelf-life, lasting scarcely longer than the time it took to get pictures of the three soldiers singing, at Mr Jackson's prompting, "Free at last, free at last," on last night's television news.
Mr Jackson, who insisted his mission did not have the approval of President Clinton, whom he counselled last year on his problems over Monica Lewinsky, apparently convinced Mr Milosevic that releasing the soldiers would soften US public opinion, and possibly the US president as well.
The success of recovering the prisoners also removes a problem that has confronted Mr Clinton in his handling of the assault on Yugoslavia. It remains to be seen if the US president, desirous as he seems to be of ending this increasingly politically fruitless crisis, can really negotiate with a man whom many in Nato wish to see standing in the dock of a war- crimes tribunal.
None of this is likely to trouble Mr Jackson, whose handling of media relations under fire in Belgrade has been impeccable and who has, once again, given proof of the power of prayer, provided the right people are doing the praying.
Julian Manyon is an ITN news correspondentReuse content