Victoria Azarenka's bid to hold on to her Qatar Open title, and the world number one ranking, began with victory over herself, a treacherous wind, world number 62 and Romina Oprandi on Wednesday.
Azarenka's 6-2, 6-3 success was encouraging both in the way she responded to being within a point of losing the first three games in irritating conditions and for her maturing sense of adaptability.
There were moments when the 23-year-old resorted to cursing and racket swishing, but Azarenka's frustration never got out of control and her grip on the match increased as her mind imposed its focus.
With Serena Williams' fitness still the subject of speculation, and with Maria Sharapova needing both Williams and Azarenka to falter if she is to regain the pinnacle, the top-seeded Belarussian could yet hang on to the top spot.
"It was a little bit of a slow start, and I had to adjust," Azarenka said.
"I couldn't go for my shots, and I had to be a bit more patient. She (Oprandi) is tricky and plays so many different balls that you don't know what to expect. I had to focus more and move my feet more."
The title-holder also took satisfaction from her ratio of successful moves to the net, winning 15 of her 20 attempts in what is not an area of special strength for her.
"It's something I want to improve. I am solid from the baseline, so I tried to change it up a bit," she said. "I had a lot of opportunities to do that today."
It was Azarenka's first match since retaining her Australian Open title in Melbourne three weeks ago, and underlined her better physical condition than Williams.
The Wimbledon and US Open champion's strapped up ankle will be tested again on Thursday by a last-16 clash against Urszula Radwanska, the younger of the two Polish sisters.
Azarenka's last-16 match is against Christina McHale, the world number 44 from the United States.
A repeat on Saturday of her semi-final last year with Agnieszka Radwanska, the world number four, looks very possible, though she cannot hold on to the top ranking if Williams is still surviving at that stage.
Radwanska, whose intelligent, well-controlled game seems well suited to the conditions, earlier reached the last 16 with comfortable win, by 6-3, 6-2 over Anastasia Rodionova, a qualifier from Australia.
She next plays Ana Ivanovic, the former world number one from Serbia.
At least Williams can be sure that her conqueror at the Australian Open will not be troubling her again in this tournament.
Sloane Stephens, playing her first event as a top 20 player, led by a set and 5-3 but could not get past Klara Zakopalova, the world number 24 from the Czech Republic, losing 4-6, 7-6 (7/5), 7-6 (7/5).
The American also served for the match at 6-5 in the final set, and then fought back from 1-5 down in the tie-break to 5-5, but still narrowly missed her chance of tackling another big name.
Zakopalova will instead take on Sharapova.
Two other seeds were beaten, Marion Bartoli, the number nine from France, and Roberta Vinci, the number 15 from Italy, bringing the total of casualties to five so far.
An ailing Bartoli lost 6-4, 6-4 to Svetlana Kuznetsova, the former French and US Open champion who is looking livelier than last year.
Another former world number one, Caroline Wozniacki, also reached the last 16.
The athletic Dane also made a tenacious escape from 3-6 down in a first set tie-break, saving four set points altogether before beating Sorana Cirstea, the world number 31 from Romania by 7-6 (9/7), 6-0.
Wozniacki next plays Mona Barthel, the German who on Tuesday upset her fifth-seeded compatriot, Angelique Kerber.