Iraq is no stranger to tourism, with countless pilgrims visiting its religious shrines, but now the country that touts itself as the "cradle of civilisation" also wants a different kind of visitor.

Though almost entirely dependent on oil exports for government income, Iraq does play host to millions of pilgrims annually who visit its multiple shrines and holy sites, from Samarra in the north to Basra in the south.

Keen to ease a reliance on Iranian pilgrims, officials in Baghdad want to promote tourism from elsewhere, and believe visitor numbers can be increased threefold.

While tourists must struggle through Iraq's decrepit infrastructure and often-frustrating bureaucracy, including a difficult-to-navigate visa system, a handful of tour operators is bringing groups to the country.

"Every area that we've been to has been totally, totally, different," said Lynda Coney, one traveller on a trip organised by Britain-based Hinterland Travel.

"The Arab people, history, the archaeology... have absolutely grabbed me with interest," the Briton told while trudging through Baghdad's main railway station.

Since 2009, Hinterland has been taking visitors on tours of Iraq lasting nine and 16 days, with prices starting at around $3,000 (2,265 euros) for the shorter trip, plus flights and visas.

The group travels in an unmarked air-conditioned van with Geoff Hann, Hinterland's owner who has himself been making trips to Iraq since the 1970s, an Iraqi policeman for security, and a small team of drivers and guides.

They mostly try not to be noticed, do not announce where they are staying or headed, and generally have low-profile security.

By contrast, officials, diplomats and foreign company staff typically travel in heavily armed convoys of vehicles with tinted windows that zoom through Baghdad's streets.

They travel from Iraq's north, where they take in the ancient cities of Nimrud and Hatra, down through Baghdad to Babylon and on to the port city of Basra, before returning to the capital.

While in Iraq, Hinterland customers stay at hotels, though the quality of the establishments varies enormously. None of the tourists expressed any complaints about accommodation.

Hann's tour operator is one of the few that has approval from the government to organise trips. Individual tourists often struggle to obtain visas to the Arab-dominated parts of the country.