ALLINN, Estonia — With Iraq still in upheaval, I thought I'd lend President Bush a hand and visit some of our loyal partners in the "coalition of the willing" to drum up more troops.

As Mr. Bush pointed out in a presidential debate when John Kerry complained that the U.S. was going it alone in Iraq, we have 30 countries standing with us in Iraq. Actually, by next month we'll be down to 27, but if each of those nations sent 5,000 additional troops, we would nearly double the foreign forces in Iraq.

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Oops. Estonia, this lovely postage-stamp-size member of our coalition, has armed forces with a grand total of only 4,000 troops.

Still, I tried.

In his splendid office in the picturesque old quarter of Tallinn, Prime Minister Juhan Parts told me how much Estonians treasure American support. So I suggested that Estonia show its appreciation by sending, say, 1,000 more troops to Iraq.

The prime minister looked stricken.

"Estonia is small," he said, arguing that the 55 Estonian soldiers in Iraq isn't bad for a country the size of his. He added: "Concerning public opinion here, of course, nobody is for war - this is quite obvious - and 60 percent were not very much in favor of Estonian participation. ... We contributed as much as we can at this moment."

My mission had suffered a setback.

One has to respect the contributions of countries like Estonia, which has already had two soldiers killed and 15 injured. Maj. Sten Reimann, who recently returned from a posting in Iraq, said that each Estonian soldier wondered before going out on patrol each day, What am I doing here? His own answer, he said, was that bringing security to Iraq is a worthy goal.

Many others I interviewed offered a more troubling answer. A student named Sven Kukenelk put it like this: "It's like an investment for us."

By this logic, Estonia invests troops in Iraq, and then the United States will be morally bound to rescue Estonia if it gets in trouble with Russia.

Triin Tael, who was out with her baby along the cobblestone streets of Tallinn, said that many Estonians considered the U.S. and Russia to be equally bad. But, she said, they want to cultivate ties with distant Washington to protect them from neighboring Moscow.

"It is in our interest to be friendly to the U.S.," she said, "because we are hoping that the U.S. and NATO will protect us if Russia attacks."

So, on the basis of those 55 soldiers in Iraq, the U.S is now committed to using its full economic and military force to back Estonia?

"Yes," she said. "That's exactly what we think."

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By NICHOLAS D. KRISTOF

And you thought it was just 'cause they loved you so much.