A headless body found in the River Tigris in Iraq is that of a Bulgarian lorry driver, Bulgaria's foreign ministry has confirmed.
This video purportedly showed captors with a Bulgarian hostage
Officials said the identification of Ivaylo Kepov, 32, was made after DNA analysis had been carried out.
The body of his colleague Georgi Lazov, who was abducted with Mr Kepov, was found in the Tigris in July.
Meanwhile, a Jordanian businessman kidnapped at the weekend was freed on Tuesday, reportedly for a ransom.
In the case of the two Bulgarians, who were taken captive at the end of June in the northern city of Mosul, the condition for their release was of a political nature: their captors asked for the release of all Iraqi detainees.
But the US-led coalition in Iraq - which includes Bulgaria - refused to negotiate.
11 August: Body of second Bulgarian driver, Ivaylo Kepov, is identified
3 August: Turkish driver Murat Yuce shot dead
29 July: Pakistanis Azad Hussein Khan and Sajjad Naeem's dead bodies are shown on video
14 July: Georgi Lazov, 30, Bulgarian truck driver is beheaded
29 June: Keith Maupin, 20, US soldier is reportedly killed (not confirmed)
22 June: Kim Sun-il, 33, South Korean translator beheaded
12 June: Body of Lebanese hostage Hussein Ali Alyan is found dumped on a roadside
11 May: Nick Berg, 26, US businessman beheaded
14 April: Fabrizio Quattrocchi, 36, Italian security guard shot dead
In the case of Taha al-Mahrameh, a Jordanian working as the director in Iraq of a Danish food company, a ransom was reportedly enough to save his life.
The former hostage's brother told the Associated Press news agency that he would return to Jordan later this week.
"We are very happy after speaking with him," he said in a telephone interview from Jordan's capital Amman.
"He sounded OK and said he was looking forward to coming back home."
The latest incidents follow the kidnapping of an Iranian diplomat, Fereydoun Jahani, who went missing last week while travelling from Baghdad to the Shia Muslim holy city of Karbala, where he was due to take up office as consul at the newly-opened consulate.
On Tuesday, at least three Iranian reporters, including the Baghdad bureau chief of Iran's official news agency IRNA, were reported to have been detained by police in Baghdad.
"Local police have arrested three of our colleagues in Iraq," Hassan Lavasani, IRNA's head of foreign news, told Reuters news agency.
Earlier reports had suggested the men had been kidnapped by an armed group.