In Miami, union plumbers agreed last year to cut their hourly pay on some new projects by nearly $2 - from $12.30 to $10.39 - to win back jobs that had been lost to non-union crews.

In Phoenix, unions that were doing 90 percent of residential construction during the early 1970s were doing only 10 percent a few years later. In Houston, unions had 60 percent of heavy construction work three years ago; they do 30 percent today. In Washington, it is the same story for non-subway construction: two-thirds union in 1974, one-third today.

In 1970, construction unions were winning contracts with first-year wage increases averaging more than 17 percent, double the rate for manufacturing. Now construction trails manufacturing, with modest first-year increases of just over 6 percent.

These are straws in a wind that is battering the old-line building trade unions and reshaping the American construction industry, with far-reaching implications for the economy as well as business and labor.

Across the country, construction unions - carpenters, bricklayers plumbers and others who have formed the undergirding of the trade union movement from its inception - have their backs to a wall that they helpled to build for themselves.

They are fighting back, often in ways that would have seemed unimaginable just a decade ago, including wage cutbacks and freezes, relaxation of restrictive work rules and their first coordinated organizing drive in history.

But even some union leaders concede that it will not be easy - and may not be possible - to reverse the trend away from union domination of American construction.

The fate of the hard-hat unions is not just a matter of concern to labor historians.

Because of work rules as well as wages, union labor generally costs more than nonunion work, especially when competition is weak - sending a ripple effect throughtout the economy and contributing to the ebb and flow of inflation. At the same time, the unions set work quality standards that are tacitly honored even by nonunion operators.

Moreover, the construction unions, with 4.5 million members, roughly 1 out of every 3 in the AFL-CIO, have been mainstays of the American labor movement since its founding: "conservatives" with little patience for the ideologies of the left that have characterized unions in many other countries. Their fortunes are likely to affect both the strength and the direction of the entire labor movement.

According to union as well as government and industry officials, construction unions were virtually writing their own tickets during boom times in the 1950s and 1960s.

They skimmed off the biggest and best-paying jobs and left the rest to non-union constractor and workers, who captured the homebuilding market and then branched out, capitalizing on a competitive advantage produced by widespread strikes and high constract settlements in the unionized sector of the industry.

"They started doing the work our people didn't want to do and went from there," sai d Edward J. Carlough, president of the Sheet Metal Workerone of 17 AFL-CIO unions involved in construction.

"In effect, the unions priced themselves right out of the market," said an industry official.

So long as work was plentiful, the competition from unorganized workers didn't hurt the union hard-hats. Everyone prospered. But when the bottom dropped out of the construction market during the recession of the mid-1970s union as well as non-union jobs were threatened, and the competition became real.

Unemployment in the construction industry as a whole hit a high of 22.2 percent in May 1975, nearly one out of every four workers, according to government statistics that unions claim underestimate the actual jobless rate. (The government says construction unemployment hit a four year low of 9.5 percent last month, but that is still half-again as high as the overall jobless rate of 6 percent.)

With the whole industry hurting, more and more work went to those who could do it cheapest and quickest: the so-called "open shop" employer who didn't have to use union workers and thus had no worry about strikes, work rules, inflexible job classifications or union-scale pay. All in all, industry officials say it gave him a 15 to 20 perrcent cost advantage, maybe more.

"Just look at strikes alone," said an official of the Associated General Contractors, an association of both union and open-shop firms."With a billion dollar job, with the cost of money at 7 percent, it costs $265,000 a day to do nothing. You get a two week strike and you'll have some explaining to do to the chairman of the board."

"The price of everything was going up - money, materials, supplies, design, enviromental standards and litigation over them," said Robert A.Georgine, head of the AFL-CIO's Building and Construction Trades Department. "They couldn't cut costs there, so they cut the only costs they could control: the price of labor."

In other words, they went non-union, often into so-calles "double-breasted" operations , with a spin-off non-union company to bid for work that the union company couldn't get. And thousands of union workers - no one seems to know how many - "put their cards in their pockets" and went where the work was.

"After all," said Georgine, "they wanted to feed their families."

The construction industry is so fragmented and uncharted that there are no indisputable figures on the extent of unionization, but some knowledgeable sources indicate it may have fallen about 70 percent to 50 percent or less in the last decade.Union officials say the decline has been exaggerated but agree that the erosion has been serious.

Housing construction is now almost all non-union. Big commercial and heavy industrial construction remains the most heavily unionized, in large part because unions can provide the kind of manpower-on-demand that all but the biggest firms cannot.

But there are inroads there too, with several of the biggest firms, including the largest of all, Houston's Brown Root, now doing some or all of their business without unions, according to the National Constructors Association, with represents big unionized firms.

The number of non-union firms among the 400 largest nearly doubled within the past year, from 19 to 37, according to the Associated Builders and Constructors, a mostly non-union group, whose membership has grown from 3,400 to 12,000 in the past five years.

Similarly non-union construction has spread out of its home base in the South to union strongholds in the Far West, where industry sources estimate that open-shop work on projects exceeding $250,000 jumped from 16 to 21 percent over the past year. It was not by coincidence that the AFL-CIO construction unions chose Los Angeles to kick off its new drive to build up membership and meet the competition head-on.

According to the Engineering News Record, a McGraw-Hill publication, an unreleased study done for the Department of Housing and Urban Development concludes that the open shop now dominates outside metropolitan areas and will continue to grow everywhere except in downtown high-fise construction, where unions will continue to dominate.

Some industry representatvies join the Associated Builders and Contractors' John Trimmer in asserting that "the virtual control of the industry by unions has been broken," but few if any will argue that George Meany's plumbers should be put on the endangered species list.

Some see an at least partial revival of the trade unions, especially if construction activity continues to pick up and the unions start organizing and continue chipping away at non-competitive work practices.

A few, like the New York-based Conference Board, see the potential for growth of multi-craft industrial unions, thus circumventing the rigid job classifications of the craft unions.

The AFL-CIO's Georgine believes his unions have already done more than most people realize to eliminate non-productive work rules, including reducing double-pay overtime to time-and-a-half, negotiating strike-proof project agreements and making more efficient use of manpower.

"It's the trend and those that haven't been cleaned up are being cleaned up," he said.

Carlough cites some examples from his Sheet Metal Workers union: strikes our contracts reduced from 30 to 40 a year in the early 1970s to none for the last 18 months, a labor-management panel to resolve disputes, a new classification of workers at less-than-journeyman pay. "It took some persuasion and head-knocking , but we had to do it," he said. "Now there are a lot of places in the South where we're the only union on a job. Two years ago we weren't there either."

A government official who monitors contract settlements has also spotted some instances on lengthening the work week from 36 to 40 hours, trimming back coffee breaks and wash-up times ("It's a lot of time, and that can be big money") and greater flexibility in work assignments. "They're nibbles," he said, "but they add up."

A labor-management agreement to eliminate strikes and reduce featherbedding in nuclear power plant construction was announced with fanfare at the White House recently, followed shortly by a similar agreement for big industrial jobs in the South.

Organizing remains a key question. It flies in the face of a long history of trying to restrict membership, but Georgine says this can and will be reversed. The construction unions have hired away the Teamsters' construction organizer, dispatched 17 organizers to Los Angeles and targeted three or four other areas for consideration. But they are fiercely resisting Labor Fepartment hiring goals for women in construction.

"They're awakening to the problem," said Maurice L. Mosier, president of the National Constructors Association, whose fate is intertwined with that of the unions. "It would have been a lot better if it had happened 10 or 15 years ago."