As with so much else in Iran today, tourism has become a battleground between conservative and liberalising forces.
The conservatives fear the "cultural pollution" they believe tourism would bring.
They also argue that the expected revenue from tourism could just as easily be raised if the price of oil was raised by a couple of cents a litre. Iran is the third-biggest oil exporting country in the world.
The liberals, including many in the current regime of President Khatami, see tourism as a way of educating the world about their country. It would, they believe, help Iran's image abroad and go some way to countering the hostile propaganda it is so frequently subject to from the West.
A survey in 1999 found the first word that struck eight out of 10 Europeans when asked about Iran was "terror". Which is ironic, as Iran is one of the safest countries in the world.
Economically, apart from being a good way to earn foreign currency quickly, tourism would create jobs for a burgeoning youth population. Of Iranians, 44 per cent are under 15.
But in 1999 it had just 1.3 million visitors, fairly pathetic in a country which is three times the size of France, which had 71 million visitors in the same year. And most tourists are neighbouring Muslims on pilgrimage to the holy cities of Mashhad or Qom.
Worthy arguments are hardly persuasive where tourists are concerned and they are not necessary in this case. Iran is arguably one of the most interesting countries in the world, with a history that is at least as old as Egypt's and just as fascinating, and foreigners are made welcome.
Our group was frequently assumed to be American, and the people were just as friendly on discovering we were Irish. They are also generous hosts and good company, attributes one would not immediately expect of such a sober society.
And there is Esfahan, a truly beautiful wonder of the world. With an estimated population of 1.1 million people, the city is really one great oasis surrounded by mainly arid country. It was built to impress, by Shah Abbas I, in the late 1500s. Running through it is the great Zayande river which, when we were there, had completely dried up leaving a great expanse of fissured riverbed with the odd pool of water, crossed at intervals by magnificent bridges from the 1600s, some from the 13th century, with their inbuilt teahouses. And Imam Square, created in 1612, which is twice as large as Red Square in Moscow, with its countless shops and wonderful mosques.
By any fair reckoning the Imam mosque must be among the finest buildings in the world. It is covered in pale blue tiling which takes on different shades as the light changes through the day. Designs are complex and geometric, underlining a local view that "God is a mathematician".
If Esfahan is beautiful, Shiraz is probably more popular with Iranians. Described as the country's "poetical capital" it is where Iran's two great poets, Hafez (14th century) and Sa'di (13th century), are buried. Hafez was a fine lyric poet whose words have entered the love lives of the remarkably romantic Iranians to a unique extent.
His mausoleum is one of those "tender spots" people visit to mark some deep feeling. When we were there, busloads of women arrived from the Caspian area, three days' journey away. They were the mothers, sisters and lovers of men who died in the Iran-Iraq war and had come to remember their dead.
We were advised not to sympathise with them as it was considered an honour to have a "martyr" in the family. "I am happy for you," is the accepted salutation. Whatever the honour the grief was evident. And with typical generosity, one mother gave her son's scarf, which she had been wearing, to a female member of our party.
But it is Persepolis, "`Persia city" in Greek, which draws most superlatives in what is in so many ways a superlative country. About 60 km from Shiraz, it was built as a summer capital by Darius, beginning about 521BC, and was centre of the Persian empire.
Destroyed by fire under Alexander the Great in 313BC, it is still possible to experience the awe and splendour of its heyday among the exotic ruins. Nothing from the ancient world, outside of the pyramids and the Valley of the Kings, is quite as impressive.
And of course there is Tehran. A sprawling city of nine million people, with three million more commuting daily, it is heavily polluted. The streets are jammed with Paykans, locally-made cars, which spew out fumes and weave through the city streets honking at anyone ) who gets in the way. But it also has the National Museum of Iran, the Islamic Arts Museum and the National Jewels Museum which has a huge display of some of the most vulgar pieces of all that glisters in the world.
And there are the Shah's boots, the remains of a 20-metre bronze statue of the former ruler, next to his palace.
The rest was melted down and "used for bullets" according to a local. What remains are the six-metre boots, indicating "all he left to Iran!".
