David E. Hoffman is the author of "The Dead Hand: The Untold Story of the Cold War Arms Race and Its Dangerous Legacy," which won the Pulitzer Prize for general nonfiction this week. This is from The Washington Post.

The number of nuclear weapons in the world has fallen from more than 60,000 at the peak during the Cold War to about 23,000 today, of which 95 percent are in the United States and Russia. Yet even with the signing of the new strategic arms accord last week, we are still left with thousands and thousands of nuclear weapons that do not make us any safer.

The agreement signed in Prague on Thursday by President Barack Obama and President Dmitry Medvedev of Russia sets a ceiling of 1,550 nuclear warheads for each country by 2017. Obama has all but acknowledged that this number of warheads remains high only to keep the U.S. arsenal about the same size as Russia's.

His nuclear posture review warned that "large disparities in nuclear capabilities could raise concerns on both sides and among U.S. allies and partners, and may not be conducive to maintaining a stable, long-term strategic relationship, especially as nuclear forces are significantly reduced." In other words, we can't go lower without Russia going lower, too.

So we remain higher than we need to.

What's behind this calculus is the old Cold War idea of counterforce: Our warfighters have to be prepared not just to threaten Russian cities but to target their numerous strategic forces.

We find ourselves in a time warp. In an age when our countries are not adversaries, we cling to an old concept because the other side does as well. The nuclear posture review stated that the United States and Russia "still retain many more nuclear weapons than they need for deterrence." In a paper last year, the Federation of American Scientists called for scrapping counterforce and adopting a new "minimal deterrence" mission that would make retaliation after nuclear attack the sole purpose of nuclear weapons. This would naturally lead to far fewer warheads than the Prague treaty allows. Obama, despite his calls for a nuclear-free world, has not gone that far.

The question "How much is enough?" has echoed through the decades. If the purpose of nuclear weapons is deterrence, it may be impossible to answer definitively, and the disagreements are wide. But in the latest issue of Strategic Studies Quarterly, three Air Force thinkers offer a surprising estimate. James Wood Forsyth Jr., Col. B. Chance Saltzman (chief of the Air Force Strategic Plans and Policy Division) and Gary Schaub Jr. conclude that "America's security can rest easily" on a comparatively small nuclear force - perhaps numbering only 311 nuclear weapons. They point out that China has already moved to a minimum deterrence strategy with an estimated 400 warheads, and 200 deployed.

By contrast, even with this new treaty, the United States and Russia are still stewards of large piles of nuclear warheads. The agreement doesn't cover 2,500 tactical or battlefield nuclear weapons still hanging around (500 held by the United States and about 2,000 in Russia). Nor does the treaty restrain the additional estimated 2,500 warheads contained in the "hedge," or reserve, maintained by the United States. And there are another 4,500 U.S. warheads awaiting dismantlement. Obama has promised to move on all of these fronts - in the future.

Once, during an internal Kremlin debate over missiles, Vitaly Katayev, a staffer in the Central Committee of the Soviet Communist Party during the last two decades of the Cold War, implored a deputy chief of the General Staff to realize that the Soviet Union had overdone it.

"Unbeknownst to everybody," Katayev insisted, "the time has arrived when the accumulation of nuclear weapons has outgrown its own level of safety and . . . both our own nuclear weapons and those of the Americans have turned from being a means of deterrence into an instrument of increased danger."

It has been a quarter-century since Katayev made that case. This week world leaders gathered in Washington for a summit on nuclear security, knowing that today's threats are far more diffuse than in the past - and far less likely to be deterred by nuclear weapons. Without the burdens of the Cold War to hold us back, we are terribly tardy in cleaning up its legacy of nuclear overkill.