We're in an upper room in a modest concrete block building on the Brooklyn waterfront. It's in the Red Hook section, across Buttermilk Channel from Governor's Island and the lower tip of Manhattan Island.

The sovereign State of New York will take testimony from conflicting advocates about a waterfront problem this morning in this seamen's haven near the docks.Pool tables have been pushed to the side; Ping-Pong tables are folded and leaning against the wall.

The Stella Maris Seamen's Center is run by the Roman Catholic Diocese of Brooklyn, so there's a tiny chapel off the pool room. A red votive light burns behind the altar, just out of the view of dockworkers leaning against the wall, waiting. They are dressed in light graybusiness suits now. They are union officials and stevedoring company executives, but they are dockworkers to the bone; hard-handed, Camel-smoking dockworkers.

Eileen Dugan, a New York State Democratic assemblywoman who speaks for the Red Hook section in Albany, the capital, bustles in with an armload of papers. She quickly opens two gray plastic tablecloths and spreads them on lunch tables.

Where's your name plate, Steve? she snaps out to a man next to her. He produces a plastic placard that says: Stephen Di Brienza. He smiles at Ms. Dugan and inserts his name in a holder on the table. Mr. Di Brienza speaks for Red Hook in the New York City Council.

Both legislators are here to champion the Red Hook Container Terminal and to slam, in legislative language but slam nonetheless, the Port Authority of New York and New Jersey, owners of the terminal.

Mr. Di Brienza joins Ms. Dugan in dressing the place up. He moves to the back of the room, picks up a small round card table and carries it upside down over the heads of those already seated at the tables Ms. Dugan has covered.

This is for the witnesses, Mr. Di Brienza explains to the four or five reporters lounging in the front row.

The formal presentations begin. The mood in the room shifts from the informality of Ms. Dugan spreading the plastic tablecloths and Mr. Di Brienza carrying furniture.

Now we're into TEUs.

TEU is maritime industry jargon for 20-foot-equivalent unit. It's a measurement of containers or boxes carried on ships, and to belabor the thing a trifle further, one box 40 feet long is equal to two boxes 20 feet long.

A few days before this, James Costello, president and owner of Universal Maritime Service Corp., the stevedore that operates the Red Hook Terminal, was quoted in a paper as saying Red Hook was handling 85,000 containers a year.

Contrary to recent press reports, says Robert N. Steiner, a port authority deputy director, Red Hook . . . handled some 60,000 containers in 1987.

Of course, the discrepancy has come about because Mr. Costello was talking TEUs and Mr. Steiner was talking boxes, 20-footers and 40-footers.

What is this TEUs? says Louis Valentino, a lobbyist for the International Longshoremen's Association. Mr. Valentino, a longshoreman who has risen through the ranks in his union continues:

What is all this talk about TEUs and 40-footers? Who cares? You want to know what's going on? Listen, that's all. Look out the window. Are we busy here, or what?

From outside the window comes the angry roar of a huge diesel engine revving up. A giant end-loader snatches a 40-foot box, lifts it high and speeds down the dock toward a waiting ship.

Mr. Valentino says Red Hook Terminal already handles as many boxes as the port authority forecast says it would handle in the year 2010.

Red Hook is bursting, he says. Soon it will be too crowded to handle the boxes. There will be delays and shipowners will go somewhere else.

They'll float away, says Universal Maritime Service's Mr. Costello, and I'll float with them.

The Red Hook people and their advocates want the port authority to fill in a 30-acre basin dug into the Brooklyn shore years ago when ocean cargo moved across the old-fashioned finger piers. The fill would add new dock space for ships, and a wide storage area for the boxes.

Now, we need geography, says Mr. Costello.

The first step in the filling project is to follow federal law and study the impact such a fill would have on fish and wildlife.

Maybe we'll find there's an elephant grave down there, says Mr. Valentino. Who knows? But let's get going with the study.

The study would cost slightly less than $200,000 and could take as much as three years.

Red Hook proponents are particularly angry with the port authority for refusing to put up the money for the study.

If the port authority won't finance the study, we'll do it with volunteers. We'll do it in Albany. But we'll do it, says Ms. Dugan, the assemblywoman.

In Red Hook, it's a matter of jobs. Some 600 dockworkers are employed at the terminal. Most of them walk to work down the neat and clean Brooklyn streets their fathers and grandfathers walked.

Ms. Dugan, Mr. Di Brienza and the other New York legislators say the port authority is abandoning New York docks for the wide meadows of New Jersey on the far shore of Newark Bay.

If I were a suspicious man, says Mr. Valentino, I would say the port authority is more interested in real estate in New York than in the docks.

Mr. Steiner says a port authority market study on prospects for Red Hook will begin in six months.

Six months, scoffs Mr. Valentino. The port authority on any given day knows how many green bananas there are in the whole world.

You build the terminal first, then you go after the business. That's how everyone in the country is doing it, and that's how the port authority did it over in Jersey years ago. Never mind the market studies. Let's fill in the basin, he says.