President Obama’s Tuesday speech was intended to convey that he is taking a more measured approach to counterterrorism, reducing drone strikes and moving toward closure of Guantanamo Bay.

In many ways, the speech is excellent. The president’s effort to put the terrorism threat in context and his argument that the war cannot be unlimited and unending are praiseworthy, as is his mention of ultimately repealing the Authorization for Use of Military Force.

That said, he still claims almost unlimited war powers based on secret legal reasoning. He still has not told us what countries and groups he claims authority to attack in the name of counterterrorism, or his administration’s legal rationale for doing so.

Members of Congress should not rest on the president’s assurance that they have been “briefed on every military action.” Presidents rarely restrain themselves. Congress should limit the president’s power to kill and detain suspected terrorists, starting by providing the legal end date for the war justifying those powers.

Although the President didn’t mention it in the speech, a big policy change accompanying it is likely to be that the standard now governing drone strikes against U.S. citizens will apply to everyone. Reports hold that this new secret guidance will “sharply curtail” or “dramatically ratchet down” strikes outside war zones, ending signature strikes (killing suspicious people with drones when we are not sure who they are). Hopefully that’s right, but it seems dubious. We do not know how restrictive the current standard is—to what extent it lets the president do what he wants. The rules, at least what leaked in February, were not minimum requirements for strikes on U.S. citizens but assurance that current procedures were legal. Nothing publicly released rules out strikes undertaken by some less restrictive process. And, as a bureaucratic procedure, not law, there is no reason that the President cannot change the standard in secret tomorrow or why the next president should use it.

Apparently, the administration will also shift control over all drone strikes from the Central Intelligence Agency to the Pentagon, meaning Joint Special Operations Command, unifying the two programs. This is minor good news. CIA is better off without paramilitary jobs. More important, the shift could improve oversight and generate greater government debate about strikes. Internal controls on Pentagon strikes are somewhat more robust. Also, while the Pentagon can avoid disclosing action to Congress more easily than the CIA by claiming that they are part of “traditional military activities” requiring no presidential finding, Congress can manage the military better. That is because the Armed Services Committees, as authorizers, have more power over the Pentagon than the Intelligence Committees have over the CIA.

Congressional oversight, however, requires Congressional interest in using its powers, which has been absent lately when it comes to foreign policy. Last week, several Pentagon officials testified before the Senate Armed Services Committee that they have nearly unlimited authority under the 2001 Authorization of Military Force (AUMF) or the president’s inherent self-defense power (they were unclear on which applies where) to use force virtually wherever they and their bosses want. The letter Eric Holder sent to the Judiciary Committee Wednesday contains similar, though more cautiously-phrased, claims. This is not new. What was surprising was that the Senators on the panel requested that the officials provide a list of groups that the AUMF supposedly allows them to attack. Apparently, the senators, like the rest of us, have no idea what groups we are now fighting.

The administration should at least tell us in what countries and against what groups we are now at war. If they won’t, Congress should require it. They should also make the administration publicize its standards for who it can kill in drone strikes rather than just demanding secret and limited access to them. Secret oversight is an oxymoron. More importantly, Congress should put some temporal or geographic limits on the war. Better yet, it should sunset the Authorization of Military Force to coincide with the drawdown in Afghanistan. That would leave substantial authority to use military and policing powers to fight terrorism. If a president wants to use wars powers in Mali, Somalia or wherever, he should have to ask, so as to force public debate.

The White House does deserve credit for renewing its effort to close the Guantanamo Bay prison (Gitmo). In 2008, both presidential candidates recognized that the prison had become a diplomatic sore and practical nightmare that should be closed. But the Obama Administration’s effort to shift its prisoners to the normal legal system or other countries has stalled. Some of this was due to political missteps, especially by the Attorney General. But the real trouble was Congressional Republicans, who made Gitmo a monument to militarized counterterrorism and demanded that even alleged American terrorists get shipped there. As the Presdient said, U.S. taxpayers now pay $150 million annually to operate Gitmo. Now, Southern Command wants almost $200 million to upgrade it. We can add fiscal prudence to the reasons to close it.