President Barack Obama desires to further reduce nuclear arsenals below the levels set in the 2010 New Strategic Arms Reduction Treaty (New START). Republicans on Capitol Hill and former officials of the George W. Bush administration assert that he can reduce U.S. nuclear forces only as the result of another treaty, requiring approval by a two-thirds majority in the Senate. In fact, over the past 40 years, there is plenty of precedent—set by Republican presidents—to the contrary.

Why this matters has to do with how Mr. Obama might codify a new arms reductions arrangement with Russia. If Moscow is prepared to engage, still an open question, the Obama administration appears to want options in addition to a treaty. Why? Fear that Senate Republicans would set an impossibly high bar for any new Obama treaty, a worry fueled by the unexpectedly partisan and bitter ratification fight over New START.

For more than 40 years, U.S. presidents reduced nuclear weapons and recorded limits—or sought to do so—in ways that did not require Senate consent to ratification, starting with Richard Nixon. Mr. Nixon in May 1972 signed the interim offensive arms agreement on strategic weapons. It froze the numbers of launchers of U.S. and Soviet intercontinental ballistic missiles (ICBMs) and submarine-launched ballistic missiles (SLBMs) at levels giving the Soviets significantly larger numbers. Mr. Nixon chose to submit this as an agreement requiring a simple majority vote by both houses of Congress rather than as a treaty requiring two-thirds majority approval in the Senate.

Some 20 years later, President George H. W. Bush made deep unilateral cuts in the U.S. nuclear arsenal. In September 1991, he announced what became known as the “presidential nuclear initiatives.” These included the elimination of all U.S. nuclear artillery shells and warheads for short-range ballistic missiles, as well as the removal of all tactical nuclear weapons from U.S. Navy warships, many of which would be destroyed. Mr. Bush said that he had consulted with his senior advisors and the Joint Chiefs of Staff. He made no mention of the Senate or Congress—and appears not to have consulted with them before announcing a second set of nuclear initiatives in January 1992.

As a result of the presidential nuclear initiatives, the United States unilaterally eliminated thousands of tactical nuclear weapons from its arsenal. According to Department of Defense figures, the overall U.S. nuclear stockpile fell from more than 23,000 weapons to less than 13,000 during the Bush presidency. Only some of those reductions resulted from treaties approved by the Senate.

Ten years later, in November 2001, President George W. Bush announced that, as a result of his administration’s nuclear posture review, the U.S. military would maintain 1,700-2,200 “operationally deployed strategic nuclear warheads.” When President Vladimir Putin asked for a new arms control treaty with limits below the levels of the 1991 START I Treaty (it allowed each side 6,000 warheads), the Bush administration came up with a novel approach: Mr. Bush would state publicly that the United States would maintain no more than 1,700-2,200 operationally deployed strategic nuclear warheads, and Mr. Putin would state that Russia would maintain X. It would be up to Moscow to fill in the X at whatever level the Russians chose; the Bush White House did not care. These would be parallel statements of national policy, not a treaty subject to approval by the Senate.

This approach held little appeal for the Russians. In the end, Mr. Bush, grateful for Russian support in the aftermath of the 9/11 attacks, agreed to Mr. Putin’s direct plea for a treaty. They signed the Strategic Offensive Reductions Treaty (SORT) in May 2002, a two-page agreement that limited the United States and Russia each to no more than 1,700-2,200 “strategic nuclear warheads,” though it failed to define “strategic nuclear warhead” or anything else and had no monitoring provisions. The treaty was unverifiable.

There are good reasons to consider codifying further nuclear reductions in a treaty, particularly a treaty with agreed definitions and verification provisions. But Mr. Obama has other options, as his Republican predecessors have demonstrated. Tomorrow’s blog—“SORT vs New START: Why the Administration is Leery of a Treaty”—will address why the administration might choose an option other than a legally binding treaty.