VENICE -- A year ago, when the fear of terrorism was at its height and the dollar had fallen in value, Venice was abandoned by the foreign visitors this island city has grown to depend on for its economic health.

When it became apparent last summer that up to 75 percent of the Americans, who usually account for about half of the city's tourist income, had stayed away, Venice authorities were so distraught that they promised to pay Americans an extra 10 percent on their dollars if they would return. The promise was later forgotten.

Luckily for the Venetians, tourists are fickle and their whims easily forgotten. The depression of 1986 has turned into something of a boom in 1987. In fact, the influx of tourists, including many returning Americans, has so overwhelmed Venice this year that the very officials who last year were begging for visitors are now debating ways of limiting them to safeguard the city's heritage from what some here are calling the "new barbarians."

"There is such as a thing as critical mass in tourism beyond which this city simply cannot accommodate more visitors," said Augusto Salvadori, the city councilman in charge of the Venetian tourist department.

Salvadori, however, is vehemently opposed to a proposal revived this spring by Mayor Nereo Laroni that admission to Venice across the narrow causeway that leads from the mainland be limited to those with a confirmed hotel reservation or the holders of special admission tickets.

The idea, Laroni suggested, would be to avoid the sort of urban paralysis that occurred at Easter when an unexpected influx of more than 100,000 persons a day made walking through the city's narrow streets almost impossible.

VENICE'S NOTORIOUSLY rapacious businessmen, however, were quick to scoff at the proposal. While they publicly claimed the plan would turn their ancient maritime city into an "Italian Disneyland." their real concern seemed to be that such limited access would cut into business, which remains the Venetians' favorite pastime.

"It is all fine to try to rationalize tourism so that our city is not ruined, but it is also necessary to remember that we are a city of living people, with living needs, not just another Italian museum," said the owner of a shoe shop off the Campo San Moise.

Since the merchant class is the real power in Venice, as it was during the centuries of its ancient glory as an independent maritime republic, that sort of thinking carries weight with the city government.

"The question is really one of finding parking places for visitors' cars when they drive across the Ponte della Liberta from the mainland," Salvadori said as he sat in his high-ceilinged office in the Palazzo Giustinian on the Grand Canal. "There are only five or six days a year, such as Easter and the height of Carnival in February, when our 50-year-old parking lot at the Piazzale Roma can't accommodate the cars. On those days we must have the police out on the mainland to turn tourists back.

"After all we don't want them to drive all the way into the Piazzale Roma and then have to be turned back," he said. "That would only make them madder."

The city's real concern is not the control of all tourists, just those who contribute the least to the city's coffers. These impecunious visitors include young day trippers who cannot afford to stay in the posh hotels along the canals or pay for full-course meals at the expensive restaurants.

For more than a year now, Salvadori has been waging war against the so-called sacco-pellisti, or sleeping-bag users, who come to Venice and try to spend the night in its famous piazzas or parks. It is forbidden to sleep in public squares these days.

POSTERS BEARING reproductions of Canaletto's distinctive 18th century paintings of canal life in Venice have gone up all over the city this summer listing the "no-nos" of tourism, which range from lying down in public anytime during the day to eating picnic lunches around St. Mark's Square.

Salvadori and other city officials are sensitive to the charges that such measures are elitist, aimed only at the tourists who cannot afford the prices that have made their city probably the most expensive in Europe. The less affluent tourists, Salvadori insisted, can be accommodated in three schools that have been kept open for the sleeping-bag set.

These provide space for only 500 sleeping bags a night, at the cost of $3.50 to $8 depending on whether one sleeps under the moon or indoors.

The real face of Venice tourism is not to be found these days in the rules and spartan accommodations for those with little money to spend but in the actions of the influential Venetian Hotel Keepers Association, the true barometer of the city's economy.

In 1986, when tourists were scarce, the hotel association announced that it would not raise its already breathtaking rates for 1987. That promise was quickly forgotten when tourism showed signs of revival.

A luxury hotel like the Cipriani, where President Reagan stayed during the June summit, raised its rates to the equivalent of $500 a night for a room with bath.

"To understand Venice," said local journalist Dino Tonon this week with a rueful smile, "you must keep in mind that Venice has survived for two reasons: one,because it was surrounded by water; two, because it was always governed by pirates."