Not so long ago, the U.S. dollar was so strong that American tourists were urged to fly to London for a weekend shopping spree. With one British pound worth only a few pennies more than a single American greenback, a Burberry's coat looked cheap. (In its glory days, the pound ranged from two to four times the value of the dollar.)

But what goes up comes down: the dollar has fallen dramatically, especially against the pound, the Japanese yen and the German mark. And the question now being raised is whether the dollar has fallen too much, too quickly.

For these reasons, financial markets hang on every nuance of every phrase about the dollar that is uttered by Treasury Secretary James A. Baker III. Last week, the markets thought they heard Baker hint -- for the first time -- that he was willing to slow down the pace of the dollar's decline, at least against the yen.

Baker observed during a congressional appearance that the dollar's dip has "more than fully offset its earlier appreciation against the yen, and . . . three-quarters of its appreciation against the mark." Then he added: "We are somewhat concerned about what we think are unwarranted interpretations" that the markets sometimes put on his statement that the United States has "no target" for the exchange rate.

Of course, the declining dollar means different things in different cicumstances. Those tourist bargains in Europe have disappeared. But American manufacturers, who had complained that they were losing sales because of an overvalued dollar, heaved a sigh of relief. The trade deficit is still oppressive, but almost everyone believes that eventually Japanese and European exporters will begin to feel the pinch of higher exchange rates.

In Japan, where the yen has gone up 50 percent against the dollar in the past 15 months, the reign of Prime Minister Yasuhiro Nakasone may in time be brought to an end as a consequence of Japanese businessmen's belief that he has been outnegotiated by President Reagan. For all of the vaunted ''Ron-Yasu'' relationship, Nakasone was unable to get the one thing he wanted out of the Tokyo economic summit: a promise that the United States would help Japan stem the appreciation of the yen by a joint effort to achieve "stability."

For the United States, depressing the dollar has become the core of American international economic policy. The Plaza Hotel agreement of Sept. 22, 1985, engineered by Baker, accelerated the decline of the dollar then already under way. It was a stunning reversal of Reagan's earlier position and was applauded by all major U.S. trading partners.

But now the view among many seems to be that the Plaza agreement may have worked too well. "Weakening the dollar was considered necessary to reduce the trade imbalance," says Sony Corp. boss Akio Morita. " But the rate of change was faster and more dramatic than anybody could adjust to."

If the dollar continues to slide, it will worry Federal Reserve Board Chairman Paul A. Volcker and others, because a cheaper dollar means more costly imports, hence a new inflationary threat. Even worse, if the dollar appears to be in a "free fall," confidence in the U.S. economy may weaken, and foreign investors -- notably the Japanese -- may be less interested in financing the American budget deficit by buying Treasury securities.

So far, Japanese investment here is holding up. But this is a game played at high stakes. Shafiqul Islam, an economist on leave from the New York Federal Reserve Bank, points out that the dollar has already fallen below the level some had said would trigger a global crisis, with no dire consequences. But he suggests that the willingness of foreigners to continue to invest here is the critical issue.

Under Baker's leadership, the Reagan administration seems to be using its dollar policy as a weapon to force Japan and West Germany to serve as "economic locomotives." If they refuse to expand -- drawing in more American imports -- Baker argues the United States has no choice but to look to a depreciating dollar as the one way to force the adjustment in our trade imbalance. And in the interim, Baker says ominously, Japan and Germany risk the passage of new protectionist legislation in Congress.

If Baker's latest statement means that he is no more interested in seeing the dollar plunge out of control than anyone else, Nakasone could be forgiven for wishing that he had suggested something like that during the Tokyo summit. In any event, since Baker's testimony, the dollar has been stronger, recovering from a record low of 159 yen to about 167 yen this week. Naturally, Baker won't confirm the market's impression, but he hasn't done anything to correct it. Offically, the policy is: keep 'em guessing.