The High Representative is commanded by the European Union, the United Nations Security Council and the donor nations to implement the civilian side of the Dayton peace plan in Bosnia - more or less through sheer force of personality. "That's true ... I don't have very many weapons," he said wryly in answer to charges that he is a soft touch. "My powers are limited to political influence."
In the early days, I-For, the Nato implementation force, viewed his office with hostility (while exploiting the possibility of off-loading responsibility on to civilians), though relations swiftly improved and remain warm. Yet Mr Bildt, who is 49 but looks 10 years younger, has on occasion succeeded where the big guns of I-For failed. He persuaded the Bosnian government, for example, finally to release its prisoners of war by threatening to postpone a donor conference.
His efforts are now directed towards extinguishing the hardline flame personified by Radovan Karadzic, the president of the Bosnian-Serb Republika Srpska indicted for war crimes and shunned by Mr Bildt and I-For. Mr Karadzic is the lurking presence pervading all dealings with the Serb entity in Bosnia; he is subject to arrest by I-For, should they happen across him. Mr Bildt clearly hopes they will.
"He is poisoning the political atmosphere," Mr Bildt said in an interview in Banja Luka, where he has just opened an office, to Mr Karadzic's fury. "He is pushing isolationist policies ... and fuelling more hardline views on the other side."
The nationalist, anti-Dayton line still coming out of Pale, the mountain village near Sarajevo that is Mr Karadzic's stronghold, is exacerbating mutual fears, Mr Bildt added. "That increases the likelihood of the country coming apart even more." The former psychiatrist's continuing presence in Bosnia, despite his long-standing appointment with The Hague war crimes tribunal, "is a major provocation against the international community".
An arrest could be extremely bloody, however, given that Mr Karadzic travels with a phalanx of bodyguards, and I-For commanders are loath to intervene. "The military guidelines are very clear," Mr Bildt said. He implied that he would like to see a change of policy - from the Nato politicians who issue orders to I-For.
There is a clear moral tone to the High Representative's views, as well as a practical concern. Pursuing war criminals matters, he said. "I don't think you can establish a normal political life before that's done," he said, adding that the tribunal would face a "difficult balancing act" over how far to extend its indictments.
"How you draw that line will be tremendously important for this country," he said. "You must take away a sufficient number of people to establish justice but at the same time you must leave the war behind you."
Mr Karadzic would disagree; so Mr Bildt is bolstering internal Serb opposition this week by opening his Banja Luka office. The city is flooded with dignitaries at the moment, including John Kornblum, the US special envoy, whose predecessor forced through the Dayton agreement, and other foreigners urged to visit by Mr Bildt.
In Banja Luka, traditional political rival to Pale and home of Rajko Kasagic, the moderate Serb Prime Minister, Mr Bildt hopes to capitalise on the different perspective. "Some of them are genuinely willing to work within the Dayton framework," he said, while admitting that the peace plan was written in such a way that it is open to liberal interpretation. "Everyone is trying to twist the agreement to suit their long-term aims ... it has great potential to be twisted."
He seems particularly angered at the financial games being played: the Serbs' refusal to attend the donors' conference, and their rejection of a large seed-planting programme funded by the EU. But there is also the refusal of the World Bank to extend a project granting 10 deutschmarks per month to needy families across the line from the government side.
"I think that humanitarian programmes should apply to people in need everywhere, but the World Bank does not seem to share that view," he said acidly. The political point being, "if we go in here and start to co-operate with people they will find that productive and we will gradually break down the barriers of isolation". This is partly why Mr Bildt will be loath to use the one real weapon he has: the re-imposition of economic sanctions on Republika Srpska.
Admiral Leighton Smith, Mr Bildt's military counterpart, not only had an easier task - the separation of the warring factions - but a far bigger armoury. Mr Bildt is supposed to rebuild Bosnia, to bring in foreign money, encourage refugees to return home and ensure that fair elections take place, aided by a (so far non-existent) free press.
It is not surprising, therefore, that Mr Bildt has kept his position as chairman of the Swedish Conservatives and his homes in Stockholm and Brussels. Despite the energy and intellectual rigour with which Mr Bildt pursues his mission, he is well aware that, as one analyst cynically put it, "he is the designated loser".