The parts of the Iran nuclear agreement that would lift sanctions are among its most complicated and controversial elements, partly because there is disagreement about what effect the sanctions have had on Tehran’s nuclear program.

There is no doubt that the international economic sanctions put in place since 2005, primarily by Congress and the Obama administration working together, have “helped bring Iran to the [negotiating] table” and “in the words of Iranian President [Hassan] Rouhani . . . threatened to drive Iran back into the Stone Age.”

That was Juan C. Zarate, George W. Bush’s deputy national security adviser for combating terrorism and now chairman of the Center on Sanctions and Illicit Finance at the Foundation for Defense of Democracies, testifying Thursday before the Senate Foreign Relations Committee.

“The financial constriction campaign which began against Iran in 2005 has proven effective over the past decade not because Iran was hermetically sealed with naval blockades or classic trade embargoes, but because it was unplugged from the elements of the global financial and commercial order,” Zarate explained.

However, as effective as the economic sanctions were, they did not stop Iran from becoming “a threshold [nuclear] state,” as Energy Secretary Ernest Moniz put it Wednesday at a Senate Armed Services Committee hearing on the agreement, known as the Joint Comprehensive Plan of Action (JCPOA).

The International Atomic Energy Agency (IAEA) “has labeled Iran as having had a structured program of activities relevant to nuclear weapons in the past,” Moniz said, adding, “The [JCPOA] deal will walk them back from that [nuclear] threshold and give us permanently more insight into . . . any weapons program they might choose to pursue.”

In short, although the tough sanctions had a deep economic effect on Iran, they did not stop the country’s leaders from pushing ahead with their nuclear program.

Where Zarate emphasized problems he saw in the JCPOA, the other witness at Thursday’s Senate hearing, Richard Nephew, who served as the State Department’s principal deputy coordinator for sanctions policy and the lead sanctions expert for the U.S. team negotiating with Iran, saw opportunities.

Both, however, agreed on one thing: Additional sanctions by the United States would not reverse Iran’s nuclear program.

Nephew said, “I do not believe U.S. sanctions would stop Iran’s enrichment program from moving.” Zarate added: “I think U.S. financial power and influence is enormous and would have an impact. Would it stop a nuclear program alone? I don’t think so.”

So what are the sanctions disputes related to the JCPOA?

Foreign Relations Committee Chairman Bob Corker (R-Tenn.) at Thursday’s hearing focused first on “whether or not the U.S. can reimpose sanctions lifted in the agreement, should we need to use them for terrorism purposes,” an issue raised by several critics.

A section of the JCPOA says the U.S. administration “will refrain from re-introducing or re-imposing the sanctions . . . that it has ceased applying under this JCPOA” or “imposing new nuclear-related sanctions.”

“The United States will still be able to pressure banks and companies into not doing business with the IRGC [Iran’s Revolutionary Guard Corps], Quds Force [the Revolutionary Guard’s overseas operations force], Qasem Soleimani [the leader of the Quds Force], and Iran’s military and missile forces, as well as those who facilitate their business,” was Nephew’s response to Corker at the hearing.

Defending the agreement he had worked on, Nephew said, “The United States retains a number of sanction authorities that will continue to exact consequences for Iranian violations of human rights and damage Iran’s ability to engage in terrorism financing.”

He added, “The United States will also retain its ability to impose sanctions on those trading with Iran in conventional arms, as well as with respect to ballistic missiles, even after U.N. restrictions lapse.” That is because those issues are covered by executive orders not related to Iran’s nuclear program.

Nephew was referring to nonnuclear-related U.S. and U.N. sanctions that will remain in place if the JCPOA is implemented. These include the freeze on Iranian government and private financial interests in the United States, prohibition of U.S. persons and companies from engaging in business transactions with Iran and its entities, and export controls on U.S.-origin goods and technology or items relevant to Iran’s missile program.

Under terrorism, counter-proliferation, missile and human rights authorities, the United States will continue sanctions on third parties, including the Revolutionary Guard Corps and its leaders, who appear to be released under the JCPOA.

Zarate spoke of weaknesses in the nuclear deal’s “snapback” provision, which would permit the majority of an eight-member joint U.N. commission to reimpose sanctions based on any allegations that Iran was cheating.

Calling it “a blunt instrument,” Zarate said, “It will only be applied if the most egregious violations can be proven openly and convincingly to all parties.”

Nephew, on the other hand, called for using the joint commission for “more modest sanctions snapback,” even for minor violations, because “the Iranians need to understand that we will respond at all times . . . challenging them when we see things that are inconsistent with the terms of the deal.”

One critical element that I wrote about last week — Iran’s earlier nuclear weapons research, the possible military dimensions (PMD) issue — will be examined by the Senate Foreign Relations Committee on Wednesday. IAEA Director General Yukiya Amano is scheduled to meet privately with committee members to discuss his confidential agreement with Iran to deal with remaining questions about Tehran’s past activities, including the military base at Parchin, where testing of weapon elements allegedly took place.

Critics of the JCPOA have demanded to see the text of the IAEA agreement, claiming it is a secret side deal. The IAEA maintains that such inquiry agreements are confidential between the agency and the countries involved. Undersecretary of State for Political Affairs Wendy Sherman, a top Obama negotiator with Iran, was permitted to read the text but not allowed to keep it. She has briefed others, including members of Congress, on its contents.

Whether Amano’s presentation will satisfy critics remains to be seen. But under the JCPOA, unless the IAEA has verified that Iran has settled all outstanding PMD matters by adoption day, projected to be Oct. 15, the agreement does not move forward.

For previous Fine Print columns, go to washingtonpost.com/fedpage.