In September 1991, President George H.W. Bush announced a series of sweeping measures fundamentally reshaping the American nuclear arsenal. One of them called for all U.S. ground-force tactical nuclear weapons to be returned from overseas bases and dismantled.

Similarly, all tactical nuclear weapons on surface ships and attack submarines, as well as those associated with land-based naval aircraft, were to be withdrawn.

Eight days later, President Mikhail Gorbachev reciprocated, declaring that similar steps would be taken for Soviet nuclear forces.

As a result of these so-called Presidential Nuclear Initiatives, or P.N.I.’s, thousands of nuclear weapons on both sides were ultimately taken out of service and in some cases eliminated altogether — all based on unilateral, parallel actions, and all without an arms control treaty.

Presidents Bush and Gorbachev succeeded in bypassing the time-consuming treaty process largely because of the momentous changes taking place at the time. A year earlier, Germany had been reunited and the Warsaw Pact dissolved. The month before the P.N.I.’s were announced, Soviet hard-liners had attempted a coup against the Gorbachev regime, raising serious questions about who was really in charge of the country and its vast nuclear weapons stockpile. Crises create opportunities for bold action; both presidents rightly seized the moment.

Now, 20 years later, the subject of reducing tactical nuclear weapons has again come to the fore. Signing the New Strategic Arms Reduction Treaty in April 2010, President Obama announced that the United States intended to pursue further reductions in all categories of nuclear weapons — including, for the first time, tactical and nondeployed warheads. Voting to approve the treaty, the U.S. Senate called for negotiations with Russia to address the disparity in U.S. and Russian tactical nuclear weapons and to secure and reduce those weapons in a verifiable manner.

The specific size of that disparity is a matter of debate. Neither the United States nor Russia has publicly disclosed the number and locations of the tactical nuclear weapons they possess.

Unofficial estimates vary widely. The London-based International Institute for Strategic Studies credits the United States with 500 operational warheads, with fewer than half of those deployed in Europe. The 2009 report of the bipartisan U.S. Strategic Posture Commission cited reports that Russia has 3,800 operational tactical nuclear warheads, plus numerous reserves. Although others offer different estimates, Russian weapons clearly outnumber U.S. weapons by an overwhelming margin.

As the United States and Russia continue to reduce long-range, strategic nuclear weapons to increasingly lower levels, this disparity in tactical nuclear weapons looms larger, with potentially serious implications for the overall nuclear balance between the two countries and the continued efficacy of the U.S. nuclear umbrella for its allies.

Moreover, Russian military doctrine and public statements by senior Russian officers suggest that Moscow places high value on a large tactical nuclear force for deterrence and potential escalation in military conflicts.

Negotiating a reduction in tactical and nondeployed nuclear weapons won’t be easy. There are serious technical challenges related to verifying compliance, and U.S.-Russian differences on a range of strategic issues, especially missile defenses, cloud the prospects for “getting to yes” in formal negotiations anytime soon.

There is, however, some unfinished business concerning the 20 year-old P.N.I.’s that both governments could take up now to help lay the foundation for future talks.

The U.S. government has been quite open about the steps taken to implement the P.N.I.’s. The day after Bush’s announcement, the Pentagon provided a very detailed account of the number and types of American tactical nuclear weapons deployed abroad and on ships. More recently, in May 2010, the United States made public the actual size of its nuclear weapons stockpile for each year since 1962, as well as the specific number of weapons dismantled annually since 1994.

The Russians have been far less forthcoming. As a result, serious questions have existed almost from the outset about Russian implementation of the P.N.I.’s, as well as the role of tactical nuclear weapons in their military strategy.

By way of contrast, the United States and Russia have grown accustomed to sharing considerable information about their longer-range strategic nuclear forces. For years, they have routinely exchanged and updated information on the disposition of retiring nuclear-capable bombers and missiles. Similar processes could be applied to the types and numbers of tactical nuclear systems affected by the P.N.I.’s. Lingering doubts about actual implementation would be reduced; the overall relationship would benefit from greater openness.

The next logical step would be for both countries to disclose, on a reciprocal basis, the location, types and numbers of tactical nuclear weapons that remain.

This should pose few problems for the United States and its allies; well-informed accounts of deployed American weapons have been around for years. But disclosing such data might prove difficult for Russia, given its penchant for secrecy and the political risks of confirming it does indeed possess a far greater number of these weapons.

If such difficulties can be overcome, these two steps would enhance transparency and mutual confidence. In the process, they could help pave the way to future negotiations on reducing both tactical and nondeployed nuclear weapons.

Frank Klotz is a senior fellow at the Council on Foreign Relations. Susan Koch is an independent consultant. Franklin Miller is a principal at the Scowcroft Group and Atlantic Council Board director. All three have served in senior positions at the U.S. Department of Defense and on the National Security Council staff. This article originally appeared in the New York Times.