The class is part of a programme created by the International Committee of the Red Cross - which has a legal battlefield role in helping the victims of war - to encourage respect for the Geneva Conventions. Major Kelly's task is to convince his pupils that military as well as humanitarian benefits come from respecting the Conventions.
"Complying with the law of war will not cost you militarily," Major Kelly said. "Purely from the military self-interest aspect ... it's a smart way to operate." The humanitarian argument takes a back seat: "We do have it in there, but it's not the main selling-point."
But the two mesh quite often - a favourite example is the war in Chechnya, where the brutality of the Russian assault turned the entire population - much of which was neutral or even anti-guerrilla - against Moscow. And the Russians lost 3,000 men in the initial assault on Grozny, despite their overwhelming superiority in fire-power.
The Geneva Conventions regulate warfare quite strictly, offering legal protection of a kind to almost everyone but spies and mercenaries (though they have rights to fair trials), with particular emphasis on the safety of medical and religious staff and civil defence workers, and the right of combatants to the status of prisoner of war. Buildings such as hospitals, vital infrastructure, historical or cultural monuments and objects containing "dangerous forces" - such as dams and nuclear power stations - are also protected.
The point is that if an army respects the enemies' facilities, its own will equally be protected; if military helicopters marked with a red cross are used only for medical evacuations, both sides can ferry their wounded in relative safety. And if one side violates such conventions more often or more openly, appeals for international support for the other are more likely to succeed - a point the Bosnian Serb officers may feel keenly.
"Are the dams civilian or military objectives and who ordered their destruction? And what if there was an anti-aircraft gun installed on the dam?" one Bosnian officer asked, after watching a documentary on the Allied raids which were intended to halt industrial production in the Ruhr valley. Major Kelly replied that dams could lose their protected status if making "a direct and effective contribution to enemy operations" - the definition of a military objective.
The point, he added, was to weigh the importance of the military target against the expected civilian casualties. And his seminars are intended to teach the armies how to structure command and control, how to build a framework in which officers and their juniors can take decisions swiftly. This is essential in a region where many soldiers went to war by default, as civilians with little or no training.
The major has already worked with the Croatian army, the Bosnian Croat militia and the Bosnian army, and is due to start soon with the Bosnian Serbs. Yugoslavia is also expected to sign up. He teaches groups of officers the basics, then selects a smaller number as future trainers in each force.
Major Kelly is pleased with his pupils' enthusiasm, despite the cynicism with which many arrive. "There is a fatigue factor and a disappointment factor with what has occurred here," he said. They ask if their former enemies are also receiving such training, but there is also a readiness to discuss crimes committed by their own forces. "It's quite heartening," the major said.
Of course war by its nature is bloody; but it need not be an inexorable descent into hell. The civilians and soldiers of this region, more than most, deserve the minimum guarantees afforded by the Geneva Conventions.