Treasury Secretary James A. Baker III plays hardball. When he and Federal Reserve Board Chairman Alan Greenspan didn't see eye to eye on strategy for dealing with our trading partners, he took steps to ensure that the difference between the two men became public.

What happened was this: when Baker learned from the Fed chairman on Sept. 3 of Greenspan's plan to boost the Federal Reserve discount rate the next day (the first increase in three years), he tried unsuccessfully to persuade Greenspan to ask the Japanese and Germans to lower their rates in a coordinated action.

''It was not a big deal, not something that Baker was going to fall on his sword about,'' one official told me.

Nonetheless, the mini-dispute -- it didn't relate to basic U.S. policy -- was accurately, if a bit breathlessly, reported in The New York Times last week. ''Baker's not unhappy that it {the story} is out there,'' an administration source said.

The Fed's half-point discount-rate hike was designed to bolster the dollar in world markets. Neither Baker nor Greenspan wants to see the dollar drop any more, because that would raise a new specter of inflation here.

Moreover, as Baker saw it, coordination of German and Japanese action to lower their rates would widen differentials, reinforcing the thrust of the Fed action. And the lower German and Japanese interest rates would also help stimulate economic growth there.

But Greenspan had another view. He regarded as his first priority getting the Fed discount-rate boost on the record. And he had three fellow governors, making the necessary majority of four, on tap and ready to vote with him. The markets had wondered how strong he would be, as Paul Volcker's successor, when it came to fighting inflation.

Besides, it seemed clear that the Japanese and the Germans were not about to lower interest rates. As this week's discussions at the annual World Bank-IMF meeting indicated, the direction is the other way in those countries.

In any event, Greenspan did not want to delay the Fed's symbolic discount-rate increase while negotiating a deal with Bonn and Tokyo. So he said ''no'' to Baker's proposal, in a 90-minute session in the new Fed chairman's office that night. But the Baker philosophy is that political gamesmanship demands that ''you get something for something given,'' an insider says. ''If you make a concession, or take a step that is going to help a trading partner as well as your own country, Baker feels, well -- by golly -- you ought to get something in return, or at least try to.''

Baker felt that even if the odds were that the Japanese and Germans would turn down Greenspan's request, the proposal should have been made to establish that the United States had asked its partners to move jointly. If they said ''no,'' then the next time they were asked to help out, it would be more difficult to say ''no'' again.

What could be lost? was Baker's position. Time, was Greenspan's answer. Let's get our discount-rate increase on the books, he said in effect, and then at a central bankers' meeting scheduled for Basel, Switzerland, over the weekend, he would try to get them to lower their rates.

But by the time Greenspan got to Basel, the Fed's discount-rate hike was history. His appeal then for lower rates from the Japanese and Germans was ignored, as Baker figured it would be. Sources stress that Baker had no argument with Greenspan's decision to boost the discount rate, ''since he recognized the politics of the situation from Greenspan's point of view.''

The whole episode can be regarded as a tempest in a teapot, and surely would have been no more than a footnote in Greenspan's or Baker's future memoirs -- except for the one thing that makes this a revealing Washington vignette: Baker was not about to commit hari-kari, but he wanted the story out.

Presumably, it was Baker's way of demonstrating to Greenspan the importance he assigns to coordination of international economic policy and the need to maintain close Treasury-Fed ties.

On the other hand, Greenspan is an old enough Washington hand to have surmised that, one way or another, the modest difference between him and the secretary of the Treasury would eventually become public. If the Treasury leaked the story, Greenspan may have felt, it would serve only to underscore his intention to preserve the vaunted ''independence'' of the Fed.