On any Friday afternoon in Los Angeles, the harbor is a very crowded place. Ships from as many as eight different cruise lines are tied up to the docks in San Pedro or Long Beach. By 8 p.m. they have all departed, each heading for a three-, four- or seven-day journey south toward Mexico.

1986 may be the year of the short cruise, a relatively recent addition to the options in cruising. Eight years ago, only 500,000 passengers (50 percent of all cruise-ship passengers) took cruises of a week in duration or less. Now, more than 1.4 million (or almost 70 percent of all passengers) choose short cruises.

Nowhere -- except in Miami -- is this more evident than on the West Coast. In recent months many cruise lines -- including Princess, Cunard, Carnival and Holland America -- have positioned their ships in Los Angeles.

But the newest entrant in the crowded Mexico market may be the most attractive in terms of price and cruise options. It's called the Stardancer, a 608-foot, 1,000-passenger, 27,000-ton ship that makes three-, four- and seven-day trips to the Mexican Riviera.

One of the largest ships to cruise to Mexico this year, the Stardancer features 480 staterooms, 14 public rooms and one additional feature: It is the only cruise ship in North America that can accommodate cars and recreational vehicles on board.

Perhaps the most attractive aspect of the Mexico cruises is price. Because of the abundance in cabin space, the law of supply and demand is clearly working -- at least for now -- in passengers' favor.

Almost every major cruise ship line is now heavily discounting fares to attract new passengers. In fact, the cruise lines are scrambling to fill their ships by cutting prices by 5 to 50 percent. But Sundance Cruise Lines, owner of the Stardancer, entered the market with discount prices.

The Stardancer -- formerly called the "Scandinavia" -- is a 3-year-old ship that was purchased by Sundance last April. What followed was a marathon $5.1-million redecoration and renovation by 700 workers on 24 hour-a-day schedules that turned the ship into a luxury cruise operation that can also accommodate 350 cars and recreational vehicles.

"We are convinced this is an innovative cruise concept," said Stardancer cruise director Bruce Mabie. "This is a cruise ship with a tremendous capacity to carry vehicles. It's not a ferry that's been converted. That's why it's a special ship. We make this a cruise first."

Mabie should know. He is a veteran of the cruise-ship business, having served for years aboard Holland America ships.

"We didn't want a ship that offered what every other ship does. With the car-carrying ability, we are now finding a younger market, also lots of families with recreational vehicles are traveling with us. In fact, we're getting a market that may never have cruised before."

RV caravan groups have cruised with the Stardancer. And recently on board was a motorcycle group, "upscale business executives whose hobby was cycling," according to Mabie. The cyclists brought their bikes on board, and at each port they would leave the ship and tour the countryside, returning in time for the evening departure.

And this month a large group of DeLorean car owners will be cruising down to Mexico and displaying -- but not driving -- their cars on the ship's car deck en route.

The Stardancer leaves Los Angeles once each week, on Friday evenings, returning the following Friday morning. Passengers can board or disembark at any one of three stops en route: Puerto Vallarta, Mazatla'n or Cabo San Lucas. It will repeat this itinerary until May 16, when the ship will begin a summer schedule of similar short itineraries to Alaska.

In many ways, the Stardancer offers what many other ships do. The cabins are standard size, with twin beds and plenty of storage in both the living area and bathroom. The cuisine is surprisingly good -- there were four different kinds of fish, just for breakfast -- and a great effort has been made to "theme" the dinners -- Italian, Oriental and French.

In fact, more effort has gone into dressing the waiters for the appropriate themed dinners than in requiring formal attire for cruise passengers. As a result, a more casual, almost familial atmosphere prevails on this ship than on many others.

But the Stardancer can offer passengers certain other amenities not found on most cruise ships.

Because of the size of the ship, not only is the car deck large enough to host most convention and trade shows (even an indoor motocross has been considered), but this is one of the very few ships that allow passengers to bring their pets aboard. Passengers traveling in their RVs can bring their dogs and cats with them, as long as the animals remain in the RVs during the trip.

At selected times each day, passengers have access to their vehicles (and pets) and can feed and, yes, walk them (in an area appropriately titled the poop deck).

There are a number of other thoughtful extras on the ship. As opposed to a number of other new cruise ships, the deck space and public areas are plentiful. Despite the large passenger capacity on a recent cruise, a passenger had to really try to feel crowded on this ship.

In fact, virtually every amenity and activity offered by other cruise ships can be found on the Stardancer -- including one of the best-equipped health facilities I've ever seen and a thoughtful casino where the dealers offer lessons in the games of blackjack and roulette.

On many cruise ships, the health club seems an afterthought. Not on the Stardancer. There are 10 weight stations, Nautilus equipment, two rowing machines, four state-of-the-art exercycles, a sauna, indoor spa, two tanning beds, three massage rooms and an outdoor exercise station. But the most-used pieces of equipment are two electronic massage chairs that seem to do everything for your shoulders, neck and back except apply oil.

In addition, the Stardancer features a swimming pool area with a retractable cover. In good weather, the cover is removable in less than five minutes. In inclement weather, or colder areas, it makes the pool still usable.

Another design extra (and a definite plus) is that the ship's passenger bathrooms have heated tile floors.

"What sells this ship," said Josef Wilblinger, the Stardancer's hotel manager, "is that we offer an incredible value for the money. In fact, our prices are as much as several hundred dollars lower than other ships sailing the same routes we do."

To be sure, the Mexican discounts are substantial. Princess, for example, has discounted its Mexican Riviera cruises $600 per couple.

But the Stardancer discounts undercut just about everyone else in the market. It is virtually an unbeatable deal: A seven-night Mexico cruise from Los Angeles, with stops in Puerto Vallarta, Mazatla'n and Cabo San Lucas, can cost as little as $645 per person, double occupancy, and Sundance is offering free air fare from 57 cities through May 9.

Even more impressive, a three-night "Sun Break" cruise from Los Angeles to Puerto Vallarta sells for as little as $295 per person, also double occupancy. (The deal also offers free parking at the Los Angeles airport, transfers to the ship and air fare to or from Mexico.)

If you bring your vehicle, the fares are also quite reasonable. If your car or RV is less than 19 feet in length, the one-way fare to Mexico is $250. Fares increase by length, and vehicles 38 feet and over cost $750.

"What this means," said Mabie, "is that a passenger with a vehicle has a number of options. He can drive down to Mexico and cruise back with us, or vice versa, or he can take the vehicle with him on the ship, depart at one of the ports and reboard the ship at a later date for a return cruise. But what it also means," he said, "is that you don't have to have a car to cruise with us."

In fact, on one recent cruise, there were only 11 vehicles making the trip south to Puerto Vallarta, but the ship was nearly full with 900 passengers.

Response to the Stardancer has been almost uniformly positive. "I just decided I was going to do this," said an attorney from Minneapolis. "I booked at the last minute and I don't regret the choice. The accommodations are good, the service is good and the price is right."

On this Stardancer cruise, virtually everyone I interviewed was a first-time cruiser. In fact, it is estimated by Cruise Lines International Association that at least 70 percent of cruise vacationers are first-timers.

Perhaps the most surprising new statistic is that at least one-third of the new cruisers are under age 35. And operators like Sundance are hoping to take advantage of the changing cruise-passenger demographics.

"Shorter cruises make sense to us, because they allow new passengers to cruise, and once on the ship they will have more flexibility both in Mexico and Alaska," said Wayne McCaulley, vice president of marketing and sales for Sundance. (Many of the ships that cruise to Mexico do similar short itineraries in Alaskan waters in the summer months.)

And yet, despite the strong passenger response, there are those in the cruise industry who insist that the Stardancer concept will not work, because no one really wants to bring his vehicle to Mexico. "Yes," admitted McCaulley, "we are still feeling our way around in the Mexico marketplace. Not everyone is comfortable yet with the concept of driving their vehicles to or from, or even around Mexico. But we are confident that this will change soon."

It may take awhile, but Sundance seems committed to making the concept work. McCaulley said that Sundance is now trying to either purchase or build a second ship to meet anticipated booking response for the 1987 season.

Not surprisingly, the pundits who are pessimistic about the Stardancer's chances in Mexico are the same folks who gave the thumbs-down sign when another ship, Western Cruise Line's S.S. Azure Seas, began three- and four-day cruises to Mexico from Los Angeles more than five years ago.

Recently, the successful ship celebrated her 500th voyage.