All three delegations - the Serbs, the Croats and the Muslim-led Bosnian government - made it clear during the three weeks of negotiations that they had serious reservations about the concessions they were being asked to make. Each had its reasons for considering the proposed settlement a bad one.
The Muslims, doubtful that the deal would succeed in keeping Bosnia a united state in its pre-war borders, wanted stronger powers for the central government in Sarajevo than the settlement envisaged. They were also angry at having to accept Bosnian Serb control of almost all eastern Bosnia, especially the former United Nations-protected "safe areas" of Srebrenica and Zepa.
The Serbs disliked the fact that the settlement restored Sarajevo as a united city, with free movement of people in all areas. They wanted central Bosnian institutions to have even less power than was outlined in the settlement, doubtless so that the Bosnian Serb zone - occupying 49 per cent of the republic - could establish the closest possible ties with Serbia proper.
As for the Bosnian Croats, they were outraged at the suggestion that they should cede Bosanska Posavina, a Croat-populated piece of land in northern Bosnia, in order to accommodate the Serbs' demands for a wider corridor linking their two slabs of territory in Bosnia. In a letter to the chief US negotiator, Richard Holbrooke, the Bosnian Croat leader, Kresimir Zubak, complained that he had been excluded from negotiations on the maps and described the proposed settlement as "not satisfying even the most basic criteria of a just peace".
Ironically, the surrender of Posavina in exchange for more land for the Croats in western Bosnia was a proposal said to have originated in talks between Croatia's President, Franjo Tudjman, and Serbia's President, Slobodan Milosevic. With their eyes fixed on the wider Balkan picture, these two men have never flinched at the prospect of sacrificing certain interests of their respective clients in Bosnia.
Yet even Mr Tudjman and Mr Milosevic could not be entirely pleased with the compromises being hammered out at a military base in the American Mid-West. One important agreement allowed Serbs to stay in the Croatian region of eastern Slavonia, but it is difficult to believe Mr Tudjman really wants people who launched an armed revolt against his rule in 1991 to keep a foothold on Croatian soil.
Mr Milosevic is known to have protested at the insistence of the US - and the Bosnian government - that UN-indicted war criminals, including the chief Bosnian Serb and Croatian Serb leaders, should stand trial in The Hague. This issue remained contentious throughout the Ohio talks.
The dissatisfaction of the three sides stems from a feeling in each camp that it may still be possible to gain more from fighting than from peace, if not now then in years to come. This is particularly true for the Muslims and Croats, who turned the military tables on the Serbs in dramatic fashion last summer and believe they could have pressed on to a convincing victory.
Mr Milosevic has a more pressing interest in peace, since it would cause UN sanctions on Serbia to be lifted. But this is not to say that either he or Serb leaders in Bosnia and Croatia have ruled out the future use of armed force in pursuit of historic Serb national goals.
It is more likely that they view the wars of 1991-95 as one more chapter in the almost 200-year history of the national effort to bring all Serbs into a single state. This effort went catastrophically wrong last August with the elimination of the Krajina Serb community of Croatia, but the establishment of a Bosnian Serb political unit covering half of Bosnia is breeding hope that one day this area can be merged with Serbia.
For its part, Croatia believes it has unfinished business in eastern Slavonia and possibly in western and southern Bosnia. In those areas, ultra-nationalist Herzegovinan Croats would much rather be absorbed into a Greater Croatian state than stay part of Bosnia's Muslim-Croat federation.
The Ohio negotiations were difficult because each delegation feared it had more to lose than to win by talking peace. This was perhaps inevitable after a war that failed to produce a clear-cut victor and left all three combatants with an even stronger sense of justice on their side than when they started fighting. But it does not augur well.