Melbourne - Serena Williams said that she was "nowhere near" as good as 15-year-old Coco Gauff when she was that age as the American great reached the Australian Open third round Wednesday despite being far from her best.
The 38-year-old, one short of Australian Margaret Court's all-time record of 24 Grand Slam titles, fought off a stubborn Tamara Zidansek 6-2, 6-3.
Williams faces China's 27th seed Wang Qiang next and could meet her fellow American Gauff in the quarter-finals in Melbourne.
The former world number one and Gauff - touted as a possible long-term successor to Williams at the top of women's tennis - spent some of the off-season together.
Williams, sporting a pair of koalas painted on her nails in light of the devastation of Australia's deadly bushfires, was mightily impressed by what she saw in "fighter" Gauff.
"She's just impressive all-round, from her personality to the way she plays," said Williams, the top-earning female athlete in the world.
"I think it's just all super-impressive.
"I was nowhere near her level at 15 either on the court or off the court, not even close.
"I know kids are growing up different nowadays, so I'm not sure. But I was nowhere near as smart and eloquent as she is.
"It's nice to see."
Gauff knocked out Serena's older sister Venus out in the first round in Melbourne, having done the same at Wimbledon last year.
Venus turns 40 in June, but Serena said she will be the first to retire out of the two sisters.
"Venus will outplay me, for sure, she loves tennis a lot," said Serena, who is in the twilight of her career but has given no hint that she plans to quit any time soon.
"She works hard on it, just gets unlucky sometimes health-wise obviously."
Williams was never in serious trouble against the 70th-ranked Slovenian Zidansek in their second round match at Rod Laver Arena.
But the 22-year-old Zidansek put up resistance in the second set with Williams twice failing to break when 40-0 up on her stubborn opponent's serve.
Eighth-seeded Williams described herself as "frustrated" by her failure to bury her opponent and she half-heartedly saluted the crowd at the end.
"I was making a lot of errors. Probably the most errors I've made since the start of the year," said Williams, whose last Grand Slam triumph arrived at the Australian Open in 2017.
Williams, who has won the Australian Open seven times, thrashed third-round opponent Wang 6-1, 6-0 when they met in the US Open quarter-finals last year.
Williams dropped just three games in her opening win over Russian teenager Anastasia Potapova on Monday in Melbourne.
Results on day three of the Australian Open Grand Slam at Melbourne Park on Wednesday:
Tennys Sandgren (USA) bt Matteo Berrettini (ITA x8) 7-6 (9/7), 6-4, 4-6, 2-6, 7-5
Sam Querrey (USA) bt Ricardas Berankis (LTU) 7-6 (7/2), 4-6, 6-4, 6-4
Guido Pella (ARG x22) bt Gregoire Barrere (FRA) 6-1, 6-4, 3-6, 6-3
Marton Fucsovics (HUN) bt Jannik Sinner (ITA) 6-4, 6-4, 6-3
Tommy Paul (USA) bt Grigor Dimitrov (BUL x18) 6-4, 7-6 (8/6), 3-6, 6-7 (3/7), 7-6 (10/3)
John Millman (AUS) bt Hubert Hurkacz (POL x31) 6-4, 7-5, 6-3
Stefanos Tsitsipas (GRE x6) bt Philipp Kohlschreiber (GER) walkover
Milos Raonic (CAN x32) bt Cristian Garin (CHI) 6-3, 6-4, 6-2
Marin Cilic (CRO) bt Benoit Paire (FRA x21) 6-2, 6-7 (6/8), 3-6, 6-1, 7-6 (10/3)
Diego Schwartzman (ARG x14) bt Alejandro Davidovich (ESP) 6-1, 6-4, 6-2
Dusan Lajovic (SRB x24) bt Marc Polmans (AUS) 6-2, 6-4, 6-3
Yoshihito Nishioka (JPN) bt Daniel Evans (GBR x30) 6-4, 6-3, 6-4
Novak Djokovic (SRB x2) bt Tatsuma Ito (JPN) 6-1, 6-4, 6-2
Roger Federer (SUI x3) bt Filip Krajinovic (CRO) 6-1, 6-4, 6-1
Fabio Fognini (ITA x12) bt Jordan Thompson (AUS) 7-6 (7/4), 6-1, 3-6, 4-6, 7-6 (10/4)
Roberto Bautista Agut (ESP x9) bt Michael Mmoh (USA) 5-7, 6-2, 6-4, 6-1
Sara Sorribes (ESP) bt Veronika Kudermetova (RUS) 2-6, 6-1, 6-1
Anett Kontaveit (EST x28) bt Astra Sharma (AUS) 6-0, 6-2
Iga Swiatek (POL) bt Timea Babos (HUN) 6-3, 6-2
Carla Suarez (ESP) bt Aryna Sabalenka (BLR x11) 7-6 (8/6), 7-6 (8/6)
Elise Mertens (BEL x16) bt Danka Kovinic (MNE) 6-2, 6-0
Heather Watson (GBR) bt Kristyna Pliskova (CZE) 4-6, 6-3, 6-1
Anastasia Pavlyuchenkova (RUS x30) bt Nina Stojanovic (SRB) 6-1, 7-5
Taylor Townsend (USA) bt Jessica Pegula (USA) 6-4, 7-6 (7/5)
Ashleigh Barty (AUS x1) bt Polona Hercog (SLO) 6-1, 6-4
Elena Rybakina (KAZ x29) bt Greet Minnen (BEL) 6-3, 6-4
Alison Riske (USA x18) bt Lin Zhu (CHN) 6-3, 6-1
Julia Goerges (GER) bt Petra Martic (CRO x13) 4-6, 6-3, 7-5
Maria Sakkari (GRE x22) bt Nao Hibino (JPN) 7-6 (7/4), 6-4
Ekaterina Alexandrova (RUS x25) bt Barbora Krejcikova (CZE) 6-1, 6-3
Petra Kvitova (CZE x7) bt Paula Badosa (ESP) 7-5, 7-5
Naomi Osaka (JPN x3) bt Saisai Zheng (CHN) 6-2, 6-4
Cori Gauff (USA) bt Sorana Cirstea (ROU) 4-6, 6-3, 7-5
Shuai Zhang (CHN) bt Caty McNally (USA) 6-2, 6-4
Sofia Kenin (USA x14) bt Ann Li (USA) 6-1, 6-3
Ons Jabeur (TUN) bt Caroline Garcia (FRA) 1-6, 6-2, 6-3
Caroline Wozniacki (DEN) bt Dayana Yastremska (UKR x23) 7-5, 7-5
Qiang Wang (CHN x27) bt Fiona Ferro (FRA) 6-1, 6-2
Serena Williams (USA x8) bt Tamara Zidansek (SLO) 6-2, 6-3
Madison Keys (USA x10) bt Arantxa Rus (NED) 7-6 (7/3), 6-2