James Ward and Johanna Konta both need just one more win to reach the French Open main draw after victories in their second-round qualifiers.
British number three Ward, 27, playing in the second round of qualifying for the first time in four attempts, beat American Ryan Harrison 7-5 7-6 (7-4).
He now faces Slovenian Blaz Rola, who is 75 places higher than him at 94 in the world rankings, in his final qualifier.
Meanwhile, 23-year-old Konta battled to a hard-fought 6-4 2-6 6-3 victory over Poland's Paula Kania.
Konta required a medical time out for treatment to her back during the deciding set against Kania, but returned to take the final three games.
The Australian-born British number three stands at a career-high ranking of 102 in the world and will face Ukraine's Yuliya Beygelzimer, ranked 59 places below her, for a place in the main draw.
Compatriot Heather Watson beat American Irina Falconi 6-2 6-4 in her first-round qualifier and the British number two faces Ukraine's Kateryna Kozlova, who is 92 places below her in the world rankings, next up.
© Sportsbeat 2014