Katie Ledecky is racing herself in the 400-meter freestyle.

Yulia Efimova and the U.S. men's relay team are just glad to have a shot at a medal.

Coming back after anchoring the Americans to a relay silver on the opening day of swimming, Ledecky nearly broke her own world record in the preliminaries Sunday, setting herself up as the overwhelming favorite to capture her first gold medal of the Rio de Janeiro Olympics.

Ledecky posted a time of 3 minutes, 58.71 seconds, actually backing off a bit on the closing lap to conserve energy for the late-night final. She just missed her mark of 3:58.37 set in 2014.

No one is even close to Ledecky. The next-fastest qualifier was Britain's Jazz Carlin, who was more than 4 seconds behind.

"That's the easiest it's felt to go under 4 minutes," Ledecky said, barely breathing hard. "So that bodes well for tonight."

Efimova heard a smattering of boos at the Olympic Aquatics Stadium after winning her heat, having only been cleared to compete days before the games.

Revelations of a state-sponsored doping system in her native Russia led to Efimova being banned from Rio because of a previous 16-month suspension for doping, not to mention another positive test this year for the now-banned substance meldonium. That result was placed on hold while world anti-doping officials conduct further studies on the drug.

After appealing their penalties, Efimova and up to six other Russian swimmers were quietly approved to compete in Rio. She posted the second-fastest time in the preliminaries at 1:05.79, just one-hundredth of a second behind American Lilly King.

Stopping briefly in the mixed zone, the reigning world champion answered a single question from The Associated Press.

"Well, I don't know what to say," Efimova said, smiling and shrugging her shoulders. "I mean, I was crazy the last half-year and just don't understand what's going on and everything. I'm just happy to be here and I'm ready to race."

When pressed on criticism from rival swimmers and coaches, she smiled and walked away.

Meanwhile, the Americans made up for a debacle at last year's world championships by easily qualifying for the final of the men's 4x100 freestyle relay.

The team of Jimmy Feigen, Ryan Held, Blake Pieroni and Anthony Ervin posted the second-fastest time in the prelims at 3:12.38.

Russia was the top qualifier at 3:12.04, setting up what figures to be a thrilling, four-country fight for the gold medal. Australia and defending Olympic champion France are also in the mix after qualifying third and fourth.

Now, the real fun begins as the countries break out their big guns for the evening final. The U.S. figures to come back with Nathan Adrian, Caeleb Dressel and 18-time gold medalist Michael Phelps, who could be joined by Ervin after the 35-year-old posted the fastest individual time in the prelims (47.65).

Australia rested up Cameron McEvoy, France has Florent Manaudou in reserve, while Russia can turn to Vladimir Morozov — another of the doping-tainted swimmers given last-minute approval to compete in Rio.

The U.S. didn't even qualify for the final of the 4x100 free relay last year at the worlds in Kazan, an embarrassing setback for the world's most dominant swimming nation.

"That's ancient history, man," Ervin said.

Assuming Phelps joins the relay for the final, as he's done at the last three Olympics, he'll have a good shot to add to his already staggering haul of 18 golds and 22 medals overall.

In other preliminaries, Kathleen Baker of the U.S. was fastest in the women's 100 backstroke, China's Sun Yang led the way in the men's 200 freestyle and Camille Lacourt of France set the pace in the men's 100 back.