After tough matches in both the first and second rounds, Barthel's passage past Pironkova was far more straightforward, breaking early in both sets en route to a 63 63 triumph.
And, ominously for the rest of the draw, the German feels the best is yet to come.
"Last year was my first time on the tour and I feel like I learned so much playing all these tournaments and playing against the top players," Barthel said. "My serve has got better and I feel like my groundstrokes are better.
"Of course, last year I was playing great tennis as well, especially here, but maybe I have a little more confidence this year."
One player with no shortage of confidence at present is Barthel's next opponent, Kirsten Flipkens. Since the back end of last season, Flipkens has been in sparkling form, reaching the quarterfinals or better in four of her last five tournaments.
She was made to work hard for her latest win, recovering from the shock of losing the opening five games to defeat the wily Monica Niculescu, 26 64 60.
"The first set was really tough. She just played a really tough game with the forehand slices and coming to the net when I didn't expect it," Flipkens said. "In the second set, I started playing more aggressive because that was the only chance for me to win this match today."
World No.91 Davis played three rounds of qualifying just to make the main draw, and in the early stages it appeared the week's exertions were finally catching up with her, Stephens taking five games in a row to wrap up a comfortable opening set.
Davis, though, was far from a spent force, hitting back to capture a couple of early breaks in the second before leveling the match at one set apiece.
The decider saw Davis twice move a break ahead, only to be pegged back on both occasions. And she was made to pay for her lack of ruthlessness, as Stephens claimed a fifth and decisive break in the 12th game to close out the match.
"It was an extremely tough match and she played really well," Stephens said. "I was kind of getting frustrated here and there and in the end I was just glad to get through.
"I was really pleased with how if finished. Towards the end I was playing some of my best tennis of the match and just managed to stay calm and composed. She's played six matches - so I knew she was tired - and I just told myself, 'make a lot of balls and go for your shots when you can.'"