Those six were sentenced to 28 to 33 years for having participated in the killing of more than 1,000 Muslim men in the 1995 Srebrenica massacre.
Families of the victims said they were outraged by the move, claiming it "defies reason."
The European human rights court in Strasbourg ruled that judges initially violated the men's human rights by applying the harsher criminal code adopted in 2003 rather than the code in force when the crimes were committed.