The agreement reached between President Donald Trump and North Korean dictator Kim Jong Un in Singapore was cheered by the Trump-loving factions of the Republican party. On Capitol Hill, however, there was a clear undercurrent of confusion over the end-product as GOP lawmakers gamed out ways to place checks on future negotiations with Pyongyang out of fear that talks could spiral out of control.

Few, if any, congressional Republicans were openly critical of the statement both leaders signed at the historic summit, in which Kim committed to a vague concept of denuclearization on the Korean Peninsula in exchange for a pause of joint U.S.-South Korea military exercises and an equally vague promise for more open economic relations. Instead, they directed their concerns at Trump’s cozy rhetoric toward Kim, and plotted subtle ways to ensure that they would have input once the final, formal deal was struck.

Sen. Bob Corker (R-TN), the chairman of the Senate Foreign Relations Committee, said early Tuesday morning that Secretary of State Mike Pompeo should appear before his panel to clear up lingering questions. And he, like other Republicans, said he was unable to pinpoint specific takeaways that could lead to successful negotiations in the future.

“While I am glad the president and Kim Jong Un were able to meet, it is difficult to determine what of concrete nature has occurred,” Corker said. The senator told The Daily Beast that the president’s comments on scrapping the joint military exercises “sounded like it might have been an ad hoc statement,” later adding that Trump “has a tendency” to make remarks that “haven’t been vetted, and sometimes those things are walked back.”

Corker’s committee wasn’t the only congressional body seeking input. Sen. James Risch (R-ID) said the White House had already agreed to allow senators to attend future negotiation sessions with North Korea vis-a-vis the Senate’s National Security Working Group, which Risch co-chairs alongside Sen. Dianne Feinstein (D-CA).

The senator was quick to clarify that Congress wouldn’t be “steering” the effort, leaving that task to the president. “It is not our intent to be there on all of the meetings or anything like that,” he explained in a brief interview.

But Risch did seem eager to gain more insight into the negotiations and the trade-offs that could be made. “It is our intent to stay fully briefed at all times as to what’s happening. And at least at the outset, there may be some actual personal presence,” Risch said. “This is advise-and-consent. So it’ll be a little more than just being an observer, no question about it.”

Foreign policy is largely considered the purview of the president. And Congress is usually loathe to encroach too deeply on major ventures, lest they share the blame for the possible failures. But Trump’s dalliance with Kim has sparked some unconventional political reactions.

Republicans who have long criticized the notion of direct diplomatic outreach to autocrats have found themselves changing their tune now that one of their own is in charge. To cover for that shift, they have adopted the posture that they can serve as a veritable buffer in order to prevent a prospective deal from ending up in the gutter. That means pushing for the Senate to potentially weigh in through the ratification process on any nuclear agreement that might be produced between the U.S. and North Korea.

“If you’re talking about a nation we’ve been at war with for about 70 years, I think it would be nice to have something that the Congress concurs with,” Sen. Thom Tillis (R-N.C.) said. “But we’re early in the process. We really need to let the president do what he’s done an extraordinary job of, which is get people to the table talking for the first time ever.”

On Tuesday, many members were open about their concerns that Trump might, at least rhetorically, go too far. That manifested itself in a particularly odd and tense moment mid-day, when Sen. Cory Gardner (R-CO) insisted that Vice President Mike Pence had told GOP senators that the military exercises with the South Koreans would in fact continue, directly contradicting Trump’s announcement. Pence’s press secretary, Alyssa Farah, insisted Gardner’s account was “false.” And the senator later clarified that Pence was referring to “readiness training and exchanges” rather than the annual military exercises that have drawn the ire of Pyongyang.

Other lawmakers chalked it up to a misunderstanding. But the episode still illustrated the discomfort many Republicans feel about the possibility that Trump was too eager for a deal. While lawmakers from both parties acknowledged that the summit reduced the tensions between the two nations, the president caught heat even from his most vocal supporters.

Sen. David Perdue (R-GA), one of Trump’s most steadfast and consistent allies on Capitol Hill, said he was “troubled” and “surprised” by the concession on military exercises, which he said was “never part of the conversations I’ve been in.”

“Coordination with the South Korean military is absolutely critical,” said Perdue, who serves on the foreign relations and armed services committees. He said the apparent concession was “not as big a deal as it might appear,” though, because the U.S. could renege if North Korea’s behavior changes.

Republican lawmakers were anxious about more than just the concrete concessions. There was a bewilderment over Trump’s deference to Kim. The night before, the president had told ABC News that he “trusts” Kim, citing the fact that “his country does love him. His people, you see the fervor. They have a great fervor.” Republicans uniformly warned Trump that the North Korean regime has committed to denuclearization in previous negotiations, only to pull back on those commitments. And they urged the president to not overlook the North Korean regime’s abysmal human rights record.

“I think it’s important that we don’t lose sight of the fact that Kim Jong Un is a butcher and he is a butcher of his own people,” Sen. John Kennedy (R-LA) told reporters. “Trying to reason with someone like that is like trying to hand feed a shark. Doesn’t mean you can’t do it. But you’ve got to do it very, very carefully.”