Zeljko Obradovic's men are in Group D with Spain and Latvia, as well as the team that wins the pre-Eurobasket qualifying tournament which will take the final qualifying place on offer.
The Serbo-Montenegrins, who have produced more NBA players outside the United States than any other country, failed to even reach the quarter-finals at the Olympics and they will be anxious to make amends in front of their home fans.
"I'm very happy with this draw because I think our group is a little bit easier than the rest," Serbo-Montenegrin point guard Milos Vujanic said to PA International.
"It's very important for us to give a good image in front of our home fans following our bad results in Athens and at the last European Championships."
Winners of the four groups book quarter-final places while second and third-placed sides play elimination round games. Teams that finish last will make early exits.
Ukraine will not like their chances of reaching the elimination round after being drawn in Group A with Russia, Germany and Olympic silver medalists Italy.
Russia will have Utah Jazz sensation Andrei Kirilenko in their line-up while Germany, bronze medalists at FIBA World Championships 2002 and a side that went unbeaten in qualifying, will be led by Dallas Mavericks sensation Dirk Nowitzki.
"This is without a doubt a very strong group which will make life hard for us," said Germany coach Dirk Bauermann. "It doesn´t alter our goal to reach the next round, however."
Turkey, under coach Bogdan Tanjevic, also won all six of their qualifying games and will be expected to advance from Group B which also includes Croatia, reigning European champions Lithuania and Bulgaria.
Lithuania nearly lost in overtime of Eurobasket 2003 to Baltic rivals Latvia, and then went unbeaten in the rest of the tournament.
If Group A is not the `Group of Death', then that honour may go to Group C which is made up of Slovenia, France, Greece and Bosnia-Herzegovina.
The French captured silver at Sydney 2000 and were favourites in Sweden at the last European Championships but lost to Lithuania and were then upset by the Azzurri to miss out on the Olympics.
France coach Claude Bergeaud claimed the draw favoured France.
"It is not a bad choice for us," he told PA International.
"It was important to play tough games in the group phase so we can be well prepared for the next rounds."
If Tony Parker, the San Antonio Spurs point guard, makes himself available for this year's tournament, they will be a force to be reckoned with while Slovenia and Greece will also be expected to pass the group stage.
Bosnia-Herzegovina have proved to be extremely difficult to beat in recent seasons and could sneak into the elimination round.
The nine sides that did not come in either first or second in their groups during qualifying will take part in a tournament before the Eurobasket, and the team that wins will advancing to European Championships in play in Group D.
Israel and Hungary will be favourites to win that tournament which also includes Sweden, Portugal, Belgium, Czech Republic, Poland, the Netherlands and Estonia.
Eurobasket will be played between September 15-25 2005.
Group A: Russia, Germany, Italy, Ukraine
Group B: Croatia, Turkey, Lithuania, Bulgaria
Group C: Slovenia, France, Greece, Bosnia-Herzegovina
Group D: Latvia, Serbia-Montenegro, Spain, Qualifier