Sen. Bob Corker and Secretary of State John Kerry are both right about the Iran nuclear deal. We were “fleeced,” as Corker claims. And outright rejection by Congress, as Kerry asserts, would damage U.S. interests.

Statements by Kerry and his fellow Obama administration cabinet officials, Energy Secretary Ernest Moniz and Treasury Secretary Jack Lew, highlight the innovations, concessions, and weaknesses of the “deal” that emerged from two years of talks with the Iranians, who are descendants of the earliest chess players.

The deal deeply divides arms control and national security analysts, including the authors of this essay—often, unfortunately, along party lines. Early indications suggest that while Congress is likely to reject the deal, the House and Senate will be unable to muster the two-thirds majority needed to override President Obama’s promised veto. The deal is likely to stand, even if it wobbles. Instead of the usual poison pill amendments which are destined to fail, Congress should insist on several measures to strengthen, not wreck the agreement.

First, since the deal is dependent on an ability to verify Iranian compliance and detect and deter cheating, Congress could make its approval contingent upon being fully informed about the substance of any side deals that Iran has made with the International Atomic Energy Agency, the agency that functions as U.N. weapons inspectors.

Last Wednesday, Sen. Tom Cotton (R-Ark.) and Rep. Mike Pompeo (R-Kan.) began that process by sending a letter to Secretary Moniz and the State Department requesting information about the side deal on inspection arrangements that some senior officials claim to have been briefed on, but which Moniz argues would traditionally remain “confidential” between the IAEA and a third party. The deal, however, is no ordinary agreement, and Congress must be clear about any arrangements affecting its viability.

Second, Congress could extend its review until Tehran complies with its commitment to resolve questions from the IAEA about 12 areas of Iranian activities that could be explained only as nuclear weapons development, the so-called “possible military dimensions” of Iran’s nuclear program.

Such information is crucial to devising an effective inspection plan to assure the world that its nuclear weapons activity has ceased and will not resume. Before Congress voted to review the deal, Kerry publicly promised that Iran would answer these questions. Although he told Judy Woodruff in April that an Iranian response to the questions “has to be” part of any final agreement, the current deal defers the matter to December. Even then, there is no guarantee Iran will comply. Congress should extend its review until those issues, as promised, have been resolved. Not only would this give Congress an informed basis for evaluating the deal, it would give Tehran strong incentives to comply.

Third, Congress should approve a resolution authorizing the use force to prevent Iran from becoming a nuclear weapons state in the event of significant cheating or breakout. Senior administration officials say Obama already has “all the authorization he needs should force be an option.” But Congress should remind Iran that future U.S. presidents will be explicitly empowered to destroy—without protracted congressional debate or prior negotiation—Tehran’s effort to build a bomb.

Fourth, Congress should establish a “Team B” of independent, nonpartisan experts with access to the highest levels of intelligence to assess Iran’s compliance with the deal. As Robert Joseph, a former under secretary of state for arms control under President George W. Bush, argued in Senate testimony, such efforts helped the intelligence community in the past evaluate the Soviet nuclear threat and Soviet arms control compliance.

Fifth, Congress should authorize the Pentagon to sell Israel the means to protect itself in the event Iran breaks its promises. The weapon in question is the massive ordnance penetrator— the “bunker buster.” Allowing Israel access to it would reinforce the White House’s promise that significant Iranian cheating will not only be detected, but also punished. As Dennis Ross, the longtime Middle East negotiator for both Republican presidents and Obama has argued, “Israel can’t set back the entirety of Iran’s nuclear program without the MOP,” a weapon designed to destroy installations like Fordow, the nuclear fuel enrichment plan buried under a mountain near the holy city of Qum.

Finally, the president and senior members of his team have acknowledged that while they hope this nuclear deal might facilitate cooperation with Tehran against ISIS, the Taliban, and other areas of concern in which Tehran and Washington share interests, the deal is not contingent upon, nor does it anticipate any change in Iran’s effort to project its influence and its support for such terrorist groups as Hezbollah in Lebanon and Hamas in Gaza.

Defense Secretary Ashton Carter and Martin Dempsey, the outgoing chairman of the joint chiefs, told Congress last week that the United States expected Iran to use at least some of the more than $100 billion in its unfrozen assets to continue to foment regional instability. Congress should ensure that future presidents can step up efforts to contain Iran by specifically authorizing more funding for U.S. military training, exercises, and other operational activities. Iran must know that Washington will counter its efforts to foment terror and regional instability through proxies.

The Iran deal is flawed, but its outright rejection would not advance American interests. Congress should plug some holes and mitigate other weaknesses. Most important, it can provide Iran with stronger incentives to comply with the deal. Such an outcome would also begin to restore a bipartisan consensus so badly needed regarding a matter central to U.S. national security.

William Tobey, a senior fellow at the Belfer Center for Science and International Affairs at Harvard’s Kennedy School, is a former deputy administrator for defense nuclear nonproliferation at the National Nuclear Security Administration. Judith Miller, a journalist, is a contributing editor at the Manhattan Institute’s City Journal and a Fox News contributor.