In response to North Korea’s sinking of a South Korean ship last March, the United States and South Korea will hold a series of joint military exercises beginning next week. But the joint exercises have become as much about geopolitics and China as they are about North Korea.

Although the exercises may be adroitly executed from a military-strategic standpoint, their success in sending a political and symbolic message is less certain. As the exercises have been considered throughout recent months, the Chinese protested aggressively and created a situation that tempts U.S. overreaction — which would be especially destructive now, as Sino-U.S. relations are already strained. The Obama administration has avoided that temptation, and the handling of the joint exercises has been both reasonable and measured. But the risk remains that Washington’s tact will be misinterpreted as a major concession to Beijing. This would be a pity. In a rare act of real smart diplomacy, the Obama administration is standing by our ally, South Korea, while also taking a moderate approach to China.

After Hillary Clinton and Robert Gates met with counterparts in Seoul this week, the Department of Defense announced a series of exercises to be held in both the Yellow Sea and the Sea of Japan. In the Sea of Japan, a large-scale air and naval exercise will begin Sunday. But notably, the details of the Yellow Sea exercises, to be held at some point in the future, were not announced, leaving more questions than answers. (The locations of both seas are crucial to understanding the issue.)

Given Beijing’s strong objections to military escapades in the Yellow Sea, which it considers its territorial backyard, the U.S.-South Korean exercises take on new significance. The fear is that unless the United States stridently defies Chinese concerns, it will be seen as conceding to Beijing and setting a precedent about what constitutes Chinese territory. This perception would be overblown given the facts, but it is all the more worrisome in the context of growing Chinese naval assertiveness.

Some have speculated that the Chinese are seeking to establish their own Monroe Doctrine and see this as a chance to reinforce it. Contrary to the UN Law of the Sea, China has objected to any unapproved non-surveillance navy activity in its exclusive economic zone, which extends 200 miles from shore. Beijing has repeated strongly worded protests against exercises in the Yellow Sea, especially those involving a nuclear-powered aircraft carrier, the USS George Washington.

If the United States proceeds with a major military exercise in the Yellow Sea, a military response from the Chinese would not be unprecedented; during the 1994 North Korea nuclear crisis, the U.S. sent a similar carrier, the Kitty Hawk, into the Yellow Sea. Although China was then a lesser military power, a Chinese submarine trailed the Kitty Hawk, and the Chinese air force dispatched fighters.

But the biggest risk is not military but political: China is trying to assert sea control; Sino-U.S. relations are already rocky, especially given Obama’s adherence to an arms deal with Taiwan; under a new prime minister, Japan is questioning whether to tilt its national-security strategy toward Beijing or toward Washington; South Korea is determining how steadfastly the United States intends to defend it from its hostile Northern neighbor; and North Korea wants to know what it can get away with.

Upon examining the facts, it’s clear that the plan announced yesterday serves the United States’s primary objectives: the Sea of Japan exercise is sufficient warning to North Korea, and it is also an impressive display of solidarity with South Korea. The scale of the exercises is huge: about 8,000 American and South Korean military personnel will participate. And the United States will employ some flashy assets. The exercise will include the George Washington, which is the core of U.S. naval power, and F-22s, the best of the best among tactical aircraft. The few disadvantages of a Sea of Japan–based exercise is that the South Korean ship, the Cheonan, was sunk in the Yellow Sea, and Pyongyang lies closer to the West. Hillary Clinton announced today, however, that the Obama administration would be imposing further economic sanctions against North Korea, strengthening the U.S. stance even more. The message to Pyonyang and to our allies is loud and clear.

This approach also enables the U.S. to avoid needlessly provoking China without conceding U.S. military rights, while taking into consideration the unavoidably necessary collaboration with China regarding the Korean Peninsula. The Chinese have suffered some of their most embarrassing historic defeats in the Yellow Sea, so they’re understandably sensitive. At the same time, joint Yellow Sea exercises will follow eventually, and the Pentagon’s press secretary, Geoff Morrell, stated clearly that the United States “obviously [has] the right to navigate all international waters, conduct operations in all international waters at the time and place of our choosing.” Furthermore, China will also be a major player in the future of North Korea and in any reunification of the Korean Peninsula; therefore, our allies in Seoul could suffer more harm than benefit from outright defiance of Beijing’s concerns.

The Obama administration’s challenge now will be to convey the wisdom of this approach to China and to America’s allies. The Nobel-winning president has made this harder on himself because of his history of pacifying aggressors and distancing allies.  But in international relations, perception is reality. Had Obama been more fearsome before, he’d be more credible now.