When Peer and Williams meet on a tennis court, as they've done rather frequently lately, the American shows not a trace of empathy -- because that is the right thing to do under those circumstances.
The No. 3-seeded Williams got through a tougher-than-expected test and beat the 16th-seeded Peer 7-6 (3), 6-3 Sunday to reach the U.S. Open quarterfinals for the 10th time. It was their sixth head-to-match, fourth this year alone, and Williams has won all in straight sets.
"Every time I played Venus, I had (a) tough time, and she was always kind of killing me," Peer said with a smile. "So today was much closer."
Afterward, both women discussed what happened at the Dubai Tennis Championship in February 2009.
Peer was blocked from entering the country because of what the government said were security concerns. Williams was critical of that, first in a news conference, then -- far more publicly -- during the trophy ceremony after she won the title there.
"She was really supportive for me," Peer said Sunday. "She stood up in that final and spoke for me. ... She understands what I feel."
Williams was honored by the Anti-Defamation League last year for her stance in Dubai, but Sunday said that "in a way, I don't think it's something too huge."
No, instead, it seemed like the obvious thing to do.
"Well, I think just because of my history, too, as African-American -- my parents both came from the South in the '40s and '50s, and just, it was an outrage, really. Just like, 'Are you serious? Can you really exclude someone?' This is professional tennis in 2010. We're all athletes here. We're not politicians or anything like that," Williams explained.
"So really," she continued, "the feeling inside of me was just one of almost rage and discontent. Like, 'Is this for real?"'
Williams had made clear she would defend her Dubai title this year only if Peer were allowed to play, and the WTA fined tournament organizers a record $300,000 and told them they needed to make sure Israeli players would be able to compete.
As it happened, Peer did play at Dubai in 2010 -- and met Williams in the 2010 semifinals there. They also faced each other at Rome and Madrid this season.
In none of their encounters before Sunday did Peer ever manage to win more than four games in any set, but she made things more interesting at Flushing Meadows. Peer probably must have thought she deserved to take the opening set Sunday, because she broke Williams' big serve twice and played solidly, making only 13 unforced errors, three fewer than the American.
Serving while down 6-5, Peer fell behind love-40, but saved those three set points. Peer would go on to save two more set points in that game, a 22-point marathon that featured eight deuces and lasted more than 10 minutes.
But two-time U.S. Open champion Williams finally found her form in the tiebreaker, taking four consecutive points -- including a service winner and ace -- to lead 5-1. There was one more blip for Williams, a double-fault at 6-2, her sixth set point, but she closed it with a big cross-court forehand that forced an error by Peer.
"Winning the first set always feels good," said Williams, whose younger sister Serena watched from the stands, "instead of having to regroup and figuring out how you're going to win the match."
That, of course, is where Peer was left, much as she always is when standing across the net against Williams.
The owner of seven Grand Slam singles titles is playing in her first tournament in more than two months, having missed time with a left kneecap injury that forced her to skip a pair of hard-court tuneup events. Before coming to New York, Williams hadn't competed anywhere since June 29, when she was upset in the Wimbledon quarterfinals by a woman ranked 82nd.
To get to her first major semifinal since Wimbledon in 2009, Williams will have to beat French Open champion Francesca Schiavone next. The sixth-seeded Italian defeated 20th-seeded Anastasia Pavlyuchenkova 6-3, 6-0 Sunday to reach the U.S. Open quarterfinals for the first time since 2003.
"When the tournament started, it was a little uncertain on ... how I would hit the ball in a match," said the 30-year-old Williams, who is 7-0 against Schiavone. "It's just very exciting to obviously be here and hitting well and getting the games on my side, so that's what I want to continue. I haven't played as much as the other players, but still I'm getting the win, so that's what's important."