The U.S. Open sought to protect the six-time champion Serena Williams, boosting her from her ranking of 26th to a seeding of 17th, out of consideration for the time she had missed after giving birth during last year’s tournament.

But the tournament’s random draw Thursday did her no such favors.

She got her least desirable possible opponent for the third round: her sister, 16th-seeded Venus Williams.

And the reward for reaching the fourth round is a possible meeting with top-seeded Simona Halep, who has surged on hard courts this summer with a title in Montreal and a runner-up finish in the Cincinnati event.

The two highest seeds who could loom in the quarterfinal round are eighth-seeded Karolina Pliskova, who beat both Williams sisters in the 2016 Open, and 12th-seeded Garbiñe Muguruza, the only active player to have beaten Serena and Venus in Grand Slam finals.

The Williams sisters have faced each other 29 times on tour, with Serena winning 17 of their matches. They have played five times at the Open: twice in the final, twice in the quarterfinals, and once in the fourth round.

Their most recent New York meeting was in the 2015 quarterfinals, when Serena beat Venus in the quarterfinals to put herself two wins from a calendar Grand Slam; she ultimately lost in the semifinals to Roberta Vinci.

In March, Venus prevailed in the most recent meeting between the pair, winning in the third round of the BNP Paribas Open in Indian Wells, California, Serena’s first tournament back from maternity leave.

While Serena’s return to the tour as a mother has drawn much attention, particularly during her run to the Wimbledon final, Venus has struggled much of this season. After reaching the final of the Australian Open and Wimbledon last year, and a semifinal in New York, Venus has not reached the second week of any major this year.

Serena has a manageable first two rounds, facing 60th-ranked Magda Linette and then the winner of the match between 120th-ranked Caroline Dolehide and 99th-ranked Carina Witthoeft. But Venus could face an uphill battle to reach the sisters’ showdown.

Venus opens against Svetlana Kuznetsova, the 2004 U.S. Open champion, who has had many highs and lows since but seems to be trending upward after winning a WTA tournament in Washington this month.

The defending champion, Sloane Stephens, seeded third at this year’s tournament after winning the title as an unseeded player last year, is also in the top half of the draw. She opens against Evgeniya Rodina, and could play Victoria Azarenka, a two-time Open runner-up, in the third round.

In the fourth round, Stephens could face 15th-seeded Elise Mertens, who beat Stephens last week at Cincinnati and reached the semifinals of the Australian Open in January.

The highest seed Stephens could meet in the quarterfinals is seventh-seeded Elina Svitolina, who has yet to reach a Grand Slam semifinal in her otherwise formidable career.

While not as loaded as the top half, the bottom half of the women’s draw features several intriguing early clashes.

Second-seeded Caroline Wozniacki, who broke through for her long-awaited first major title at the Australian Open this year, opens against Samantha Stosur, the 2011 U.S. Open champion.

Wozniacki has lost her last three matches, including an injury retirement in her first match at Cincinnati against the eventual champion Kiki Bertens, who is a possible fourth-round opponent for Wozniacki in New York. Fifth-seeded Petra Kvitova, who has won a tour-best five titles this year, is a possible quarterfinal opponent for Wozniacki.

The quarter of the draw anchored by fourth-seeded Angelique Kerber, the Wimbledon champion last month, features two potential blockbuster third-round matches: No. 22 Maria Sharapova versus No. 10 Jelena Ostapenko, both Grand Slam champions; and No. 14 Madison Keys versus No. 24 CoCo Vandeweghe, which was a semifinal in New York last year.

Rafael Nadal, the men’s top seed and defending champion, opens against a familiar opponent: David Ferrer, a fellow Spaniard whom Nadal has played 30 times on tour.

Ferrer was once No. 3 in the world, but at 36 he is now 148th and has said this may be his last Grand Slam tournament.

Nadal could face fifth-seeded Kevin Anderson, whom he beat in the final last year, in the quarterfinals this year.

Nadal’s half of the draw also includes two former Open champions who are unseeded after long injury layoffs: Stan Wawrinka and Andy Murray.

Wawrinka, the 2016 champion, begins against sixth-seeded Grigor Dimitrov, whom Wawrinka beat in the first round of Wimbledon in July.

Murray, the 2012 champion, will be playing his first Grand Slam event in more than a year.

He could face third-seeded Juan Martín del Potro in the third round.

The bottom half of the draw features second-seeded Roger Federer, a five-time Open champion who is seeking his first title in New York in 10 years.

Federer could play 30th-seed Nick Kyrgios in the third round. Federer’s likely quarterfinal opponent would be sixth-seeded Novak Djokovic, who backed up his Wimbledon title by beating Federer to win the Western & Southern Open on Sunday.