The UN sanctions prohibit transactions with a small number of Iranian banks, companies and individuals said to be directly involved in the country's nuclear programme or in support for terrorism.
But there is also a second, potentially more powerful, element. Since September 2006, US officials have been travelling the world talking to banks and company bosses. They aim to persuade business to voluntarily abandon or scale back all dealings with Iran.
Mr Levey, who is spearheading the Treasury's campaign, insists he is already getting results.
"There is significant evidence that it's working in the sense that Iranian business is being subjected to greater scrutiny and it's more difficult for them to operate," he says.
"A number of major financial institutions have cut off doing business with certain Iranian banks or with Iran entirely."
American financial pressure shows up in small ways. For example, international banks have become reluctant to issue letters of credit on Iranian trade, or only on exorbitant terms.
Letters of credit guarantee payment in international commerce. The alternative is paying in cash.
This has been going on since last September 2006. The HSBC was a major investor and handler of Iranian accounts. But, as the recent designation of IRGC as a terrorist organization (thus, all members are terrorists), one more "loophole" was closing against an organization that holds the reigns of companies that buy nuclear materials and other prohibited items.
So is American financial pressure as effective a tool as US officials claim?
Dubai is a good place to find out - a rich Gulf city that is Iran's economic gateway to the world.
A quarter of Dubai's population are Iranian and much of Iran's trade goes through Dubai. The relationship is similar to China's link with Hong Kong.
Iranian businesses in Dubai are universally reluctant to talk about such a sensitive topic. They risk offending either the Americans or the government in Tehran, more or less whatever they say.
Dubai and other international businessmen are only interested in one thing: money. They invest on that pre-requisite alone. Political, ethical nor humanitarian issues are at best, secondary concerns. Further, some businessmen are from the region don't see any ethical or political issues because a country like Iran is familiar to them in how it operates. The main concern is: is Iran stable enough that investments will see a return. At this moment, with Ahmedinijad exerting serious control over both the political and economic sectors, the answer is "yes" providing expected oil prices continue to rise and keep money in Tehran's pocket. Or, more importantly, as long as Iran can give the illusion that all is well (such as keeping $60 billion in reserve cash in a European bank while simultaneously being unable to pay workers, pay the fees for the nuclear plant at Bushehr and numerous other economically troubling concerns).
Mr Hashempore says Iranian businesses are all worried about US financial pressure, but so far, they are finding ways round it.
Mr Hashempore confirms that many Iranian firms are barred from doing deals in dollars, but they cope by switching to euros or yen instead.
He also says that many Iranian companies are able to pass themselves off as local Dubai businesses, which means they can get loans and letters of credit from international banks.
Under Dubai law, foreign enterprises are required to have a local business partner, nominally with a 51% stake in the firm.
These partners are usually paid a fee and play no active role in running the business, but for legal purposes, the firm can say it is locally-owned and thus avoid American financial pressure.
This is nothing new. Saddam was using the same loopholes to support his failing regime, purchase materials, launder money, etc, etc.
The obvious way to strangle the economy is to hit the vulnerable oil and gas industries. And yet, for international energy companies, Iran is potentially a mouth-watering prize.
European energy giants - including Shell, Spain's Repsol and Total of France - are eyeing up big up Iranian deals, as are Chinese and Malaysian oil firms. But in so doing, they all risk alienating the US, the world's only super-power.
Most oil companies do business in the US - and that would be under threat if they get too close to Iran.
There are already sanctions in place that limit investment to $20mil/year. This has greatly damaged an already aging oil infrastructure. A recent report indicates that Iran has twice the reserves of Russia, but Russia produces six times the daily output of Iran.
"What you're seeing is a strange sort of dance with some of these energy companies and they're all hoping that another company will be the first one in to become the lightning rod for the US reaction," he explains.
"The first company that does break ranks and makes a major investment will lead to an opening of the floodgates," he says, meaning that if one oil company does a deal with Iran, lots of others may follow.
So, basically, everybody is waiting for the first company to take one for the team and then they will be happy to build up the Iranian oil and natural gas fields, provide a criminal, terrorist, oppressive regime with the revenue that would sustain it for decades more.
Thanks big oil. For that reason alone, I'd be willing to support the "go green" protest the oil companies radicals.
Other Iranian Coverage:
Voice of America: Iran's Fifth Column