"The people with families have left," he said. "The old people, some of them have stayed. All the young people have left. There are very few children here.
"As for me, in terms of my religious responsibilities, my job is to be father of my people here. I have to stay with these families.
"But personally, I'm thinking about it. I'm making my preparations."
Dora's is not a precipitate flight, as so many others of Christians and other minorities in Iraq have been in 2014: a year of ethnic cleansing that capped a decade of violence and disasters. It is more deliberate, but more permanent.
"I think all our families are thinking of emigrating now," Fr Timothaeus said. "They are marking time. They think of their lives here as temporary."
Dora is a suburb of Baghdad, a city which has ironically become safer as the rest of Iraq has burned in 2014.
But it is a Sunni suburb, and in Iraq's fractured sectarian politics that means it is awash with jihadis of the Islamic State of Iraq and the Levant and their sympathisers.
The constant death threats have built on years of bombings and kidnaps to create a psychological turning point for what was once a thriving mixed community.
A decade ago, when the Americans and British invaded Iraq, there were 150,000 Christians – mostly Assyrian and Chaldean Catholics – living in Dora. With its broad if dusty streets, and comfortable villas, it must have been a decent place to live.
Now, the blast walls that snake through Baghdad turn Dora – like most of the city's suburbs – into a Russian doll of communities: Christians are surrounded by Sunnis, themselves walled off from Baghdad's surrounding Shia majority.
Just 1,500 Christians remain.
They worship at the emptying churches like Fr Timothaeus's St Shmoni's, behind barricades and army checkpoints. Every month, he says, two or three more families load their cars and quit.
The means of their gradual expulsion vary with the years. Only the end result – flight, and emigration to Sweden and America – remains the same.
Despite talks of genocide, the Christians have not been killed in large numbers this year – spared the mass shootings of thousands of soldiers, the casual killings of Turkmen Shia, the roadside murders and collective rapes of Yazidis that followed Isil's lethal sweep through the country in the summer.
But they have not been allowed to remain. In Qaraqosh, Bartella, Tel Kayf and the other Christian towns of the Ninevah plain around Mosul, they were given 48 hours to leave when Isil arrived.
In Mosul, they were told to convert or die.
In Dora, they get death threats. A note is left, telling a house's occupants they have a day to leave.
Sometimes, they are told to leave money – $800 is normal – at a named shop, if they want to remain. They hand over the money and leave anyway.
This is not new, and for some the threats follow them wherever they go – until they leave the country.
"They left an envelope with a bullet in it at my house," said Fadi, 38, a former Dora resident. "The message said, 'you are an infidel Crusader. Leave or we will kill you and your family.'
"So I left Dora and went over to my brother's house somewhere safer. They burned down my apartment and then threatened me at my brother's too."
Fadi, like many of the community, tried for a while to stay in Iraq.
When he left Dora, in 2011, he moved to Qaraqosh, Iraq's biggest Christian-majority city, in the north near Mosul.
He built a house, had his job transferred there and for a while it was a safe haven.
That was until August this year, when Isil arrived. When the church bells tolled at 1am on August 6, the residents jumped in their cars and fled in a stream of tens of thousands to Erbil.
Back at his brother's in Baghdad, his wife started getting phone calls. A jihadi had occupied their house, and found her number.
"I have taken all your possessions," the voice on the phone said. "I have all your furniture." Then the calls became more menacing. "I'm in your house, and I'm going to blow it up," the voice said.
"When I asked, 'what are you going to tell your God about this?' he replied, 'That's between me and God'," said Fadi.
The replacement by Shia militias of the leaky and demoralised Iraqi security forces in large parts of Baghdad has made the city more secure than in the summer, when it was in imminent danger from the Isil advance, and even than before then.
For years, like other parts of the city, Dora has suffered car bombs, assassinations, and kidnappings.
Fr Timothaeus recites them methodically. The car bomb at the wedding party; the sticky bomb at the police checkpoint; the churches that had been attacked – St George's, destroyed in 2004, St Matthew, the Syriac Orthodox church partially blown up by an IED, St John the Baptist, St Jacob's, St Peter and St Paul, all Chaldean Catholic churches attacked over the years.
Then there were the kidnapped priests – four in 2004-5 alone, and Fr Timothaeus's own assistant, seized in 2010, and returned only once a ransom of $80,000 (£50,000) had been handed over.
Then, on Christmas Day last year, there were the bombs at St John's Church, again, and the nearby Assyrian market. Twenty-seven people were killed.
Now, though, Baghdad is full of Christians from Qaraqosh and the other Ninevah Plain towns. Some are camping out in churches and monasteries, others stay with friends. The bombings – those targeting them directly at least – seem to have stopped.
They are grateful for the greater security the Shia militias have brought – but aware it is only a respite.
In previous years, the Shia were also the enemy. Sitting in a café in Baghdad's city centre, Issa, who asked not to give his full name, described how one cousin had been killed with his wife and son in the al-Qaeda attack on the Church of Our Lady of Salvation in 2010, and another had previously been kidnapped by a Shia militia for money.
Another cousin had lived in Mosul until he was ordered to leave by Isil on July 23. Its jihadists took his new car and $20,000 in cash as he left.
"If you stay in Mosul, you have Isil," he said. "If you move here, you have the militias. So where do you go?"
As the new Iraqi government negotiates its future with its people, in an unprecedented collaboration with its Iranian and American backers it is outlining a new form of settlement.
That involves empowering the country's regional sectarian identities: the Shia in the south, the Sunni in the west, and the Kurds in the north. If all are happy, and all have enough oil money and a certain degree of autonomy and responsibility for their own security, the theory says there will be less opportunity for militants to foment festering local grievances.
It is a plan that is being widely endorsed – except by Iraq's minorities, who see no place for themselves in this scheme. They have no militias, and under the plan, few protectors.
The Christian population, already reduced by two thirds or three quarters from before 2003, increasingly see no future here, a biblical heartland.
"This year, 2014, has made everyone eager to leave," Fr Timothaeus said, sitting in front of a small, rather forlorn Christmas Tree. "We are on the final step of the way now. Everyone wants to leave. That's it, now." The end, he says, is near.
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http://www.telegraph.co.uk/news/worldnews/middleeast/iraq/11307515/Iraq-crisis-The-last-Christians-of-Dora.html