That's when a U.S. tank shell fired from the city below smashed the room to smithereens -- killing both men.
The U.S. military initially said coalition forces were being targeted by snipers from the hotel building and were responding in self-defense. A Pentagon spokeswoman, later that same day, scolded the more than 100 other reporters working out of the same hotel who escaped injury. She said unembedded journalists -- that is, journalists not working alongside the U.S. military -- had no business being in Baghdad.
The Pentagon, in its final investigation, softened its tone. It expressed regret for the incident, calling it a "tragic and regrettable accident." But it exonerated the three soldiers in the tank who fired the round. The case was closed.
But not for Couso's family. Unhappy at the many questions left open by the case, they persuaded Spain's High Court in Madrid to open its own investigation.
This week, Judge Santiago Pedraz concluded there was evidence that the three U.S. soldiers had violated international law by willfully firing on civilians. He issued an international arrest warrant for the three men -- identified as Sergeant Shawn Gibson, Captain Philip Wolford, and Lieutenant Colonel Philip de Camp -- and said he would ask for their extradition from the United States to Spain.
Pedraz said he took the step after receiving no response to his repeated requests for cooperation from the U.S. authorities. So what happens next and will it impact diplomatic relations?
Jose Manuel Suarez Robledano, spokesman for the Professional Association of Spanish Magistrates, told RFE/RL from Madrid that the situation is legally confusing.
"At the moment, this warrant is very much up in the air because it runs up against an opposing ruling already made by the general state prosecutor," Robledano said. "So, the warrant is very debatable, and it must be confirmed by a superior court. Let's just say that the warrant is subject to, or has been put into doubt by, Spain's general state prosecutor."
Despite strong public opinion in Spain against the war in Iraq and a wave of sympathy for Couso's family, Robledano said the government is keen to avoid any diplomatic rifts with the United States -- a feeling he shares.
"Our relations with the United States must be good, they must be as good as possible as they have been for many years, and they shouldn't change," Robledano said. "And I hope that this decision does not effect our relations with a great country like the United States."
Journalist-advocacy groups, however, hope that the judge's decision may force the U.S. military to at least reopen its investigation into the Couso case and others as well.
In the past two years, more journalists have died in Iraq than in 20 years of war in Vietnam. Out of some 100 deaths, almost 20 percent have involved the U.S. military, according to Aidan White, general secretary of the Brussels-based International Federation of Journalists.
"The Jose Couso case is one which we have been following very closely," White said. "It is one of about 18 deaths of journalists and media workers since the invasion of Iraq in which United States soldiers were involved and in which there are still unresolved questions. And the failure of the United States to properly investigate all of these cases has created a deep anxiety within journalism about the rights of the victims and about the way that democratic states deal with their responsibility in this area."
White said the Couso case and the way it has been treated by the Pentagon is symptomatic of an attitude that must be changed if the United States is to maintain its reputation as a champion of democracy.
"The responsibility of the United States in this matter is a very serious one," White said. "They really have to recognize that there is genuine anxiety about the way American troops have behaved in certain incidents. They really do have to come clean about what has gone wrong, if things have gone wrong. And they've got to have independent and inclusive investigations. None of that has properly happened in the particular case of Jose Couso. The International Federation of Journalists has said that. The Committee to Protect Journalists in New York has said that. All of the press-freedom organizations are saying that. The journalists involved in the whole incident are saying that as well. The only people who are not recognizing it properly are the United States authorities. And every April the 8th, there will be protests internationally about the failure of the U.S. to take its responsibility in this matter."
A Pentagon spokesman said this week that the U.S. Central Command had no intention of reopening its investigation.
(RFE/RL correspondent Jeffrey Donovan contributed to this report.)