Havana, Cuba (CNN) -- [Breaking news update 11:35 p.m.]
Diana Nyad has broken swimmer Penny Palfrey's 2012 distance record in the Cuba to Florida swim, putting her closer to Key West than anyone has ever swum without a shark cage.
[Original story last posted at 10:18 p.m.]
Diana Nyad better than halfway through Cuba-to-Florida swim
Endurance swimmer Diana Nyad was better than halfway across the strait separating Cuba from the Florida Keys on Sunday on her fifth attempt to make it across the channel, her support team reported.
After more than 30 hours in the water, the 64-year-old Nyad was more than 63 miles north of the marina where she began Saturday morning.
"This is farther than she has gone in any previous attempt," team navigator John Bartlett wrote on Nyad's website. "Her path is only 5 miles to the east of a straight line from Marina Hemingway to Key West, thanks to a favorable Gulf Stream."
Nyad was still "swimming strongly" at just over 1.5 mph -- but averaging about 2 mph thanks to that favorable current, Bartlett wrote.
Later, her handler said that Nyad was feeling strong and coherent.
"She is joking for the first time all day," wrote Bonnie Stoll on the same website.
"The only concern is that she is throwing up everything she eats. She's quite nauseous from sea salt, but that's to be expected," said Stoll. "We're giving her enough calories and nutrition. We're just going to keep feeding her, and we hope that some of it is going down. She's not weak. Her stroke count hasn't changed."
Nyad is attempting to become the first person to swim the 103 miles without the benefits of a shark cage, flippers or wet suit. She's said it will be her last attempt at that mark, after previous attempts that were thwarted by dehydration, ocean currents and excruciating jellyfish stings to her tongue.
This time, she's wearing a specially designed prosthetic face mask to prevent the jellyfish stings.
"It took us a year; we made mold after mold," Nyad said of the mask, adding it was the kind used to protect people who had suffered injuries to their faces.
"It's a two-edged sword for me. It's cumbersome, it's difficult to swim with, but it doesn't matter. I am safe. There's no other way."
She jumped into the water at 8:59 a.m. Saturday.
Were Nyad to swim the 103 miles, it would validate her attempts, which have spanned 35 years.
In 1997, Australian endurance swimmer Susie Maroney, then 22, completed the swim from within a shark cage.
Along with the protection the cage offers against toothy predators, swimmers say the cage provides a barrier against waves and other weather hazards.
Since Maroney's swim, some of the world's best endurance swimmers have tried to cross the straits of Florida without using a cage. All have been turned back, though Australia's Penny Palfrey made it 80 miles in 2012 before unfavorable currents forced her to quit.
But few have done so as persistently or as colorfully as Nyad.
The Los Angeles resident says she feels a special bond with Cubans and hopes her repeated efforts to swim between the two countries will help improve the still-tense relations between Havana and Washington.
Nyad is being accompanied by a 35-member crew aboard two sail boats. They monitor her health, update her progress on social media and try to ward off sharks that might view her as a potential snack.
If all goes as planned, Nyad said, the swim will take her three days to finish.
CNN's Patrick Oppmann from Havana, Cuba, and Matt Sloane contributed to this report.