''Mom, they look like dead people,'' one of my daughters whispers.

It's 6 a.m. and my family is huddled on deck chairs in the pre-dawn chill aboard the Discovery Sun cruise ship. Other passengers sprawl around us under black rental beach towels, deep in slack-jawed sleep. The 20-something girl next to me is limp, her head resting on the arm of my chair.

But my two kids, ages 8 and 9, are too excited to close their eyes. As we glide away from Fort Lauderdale's Port Everglades at 8:30 a.m., our comatose neighbors stir, the sun warms our shoulders and the deck pool fills with water. The notion of swimming on a ship as it cuts through the ocean has thrilled my daughters since they saw pictures of the cruise on Discovery's website. They ignore a call for the day's first limbo contest and splash into the small, amoeba-shaped pool. The smell of fried food wafts across the deck.

Grand Bahama Island lies five hours ahead.

They're not billed specifically for families, but Discovery Cruise Line's round-trip sailings between Fort Lauderdale and Freeport are logical budget-minded getaways for people with kids. The ''getting there'' is part of the appeal. The day cruise is much cheaper than flying ($59.99 per adult, including three meals, compared to a round-trip airfare that starts at $227). Children, who cruise for free, are usually enthusiastic about exploring the ship, with its many decks, narrow hallways and staterooms, lounges and restaurants. A video arcade and kids zone help, too.

The other attraction, especially when it comes to families, is the scheduling flexibility. Passengers can come back the same day or stay several nights in a Bahamian hotel, taking advantage of one of eight Cruise 'N Stay packages offered through Discovery. Just catch the ship back on the pre-arranged afternoon of choice, almost like boarding a ferry.

ON THE ISLAND

''This was a quick, father-daughter trip for us,'' said Dragan Radulovic, a math professor at Florida Atlantic University in Boca Raton who was on the cruise as a day trip with daughter, Tatiana, 10.

The two explored the beach, swam in the infinity pool at the Westin Grand Bahama Our Lucaya Resort, and pecked around souvenir shops and stalls at the Port Lucaya Marketplace before boarding the ship back to Port Everglades at 3:30 p.m.

''We're doing a lot of bonding,'' he laughed.

Only those with stamina will want to do this in one day. Passengers are required to check in between 5:30 a.m. and 6:30 a.m. The ship doesn't return until 10 p.m., with another hour-long wait at the end to clear U.S. Customs. It's an über-long day, especially for kids.

Those with toddlers might want to consider paying an additional $65 for a cabin as a quiet refuge for naps aboard the ship. That's what the Ferlita family from Jupiter did on our trip.

While sisters Taylor, 8, and Bailey, 7, competed in the hula hoop contest in the open-air Tropical Lounge and colored in the Club Discovery kids area below deck, their brother Noah, 3, snoozed for hours with Mom in the claustrophobic but useful stateroom.

As far as cruises go, this is a no-frills ship, with industrial carpeting, cafeteria-quality food and clean but weathered furnishings. The small, hole-like pool -- filled to the halfway point with seawater -- quickly lost its appeal after my girls sloshed around in it for a few minutes.

''It's decent. You get what you pay for,'' shrugged Lori Berger of Orange County, Calif., who was on the cruise as part of a Florida vacation with her husband, Keith, and two kids, Lahna, 5, and Kai, 2.