Seeds Matthew Ebden and Andreas Seppi both suffered surprise defeats at the Geneva Open on Monday.
Nicolas Jarry upset Australian Ebden 6-2 7-6 (7-4), while Seppi suffered a similar fate at the hands of Hugo Dellien, who won 6-1 3-6 6-4.
Their exits have opened up a potentially easier route to the latter stages for Grigor Dimitrov, whose match with Federico Delbonis was postponed due to rain.
Dimitrov accepted a wild card into qualifying and has looked sharp ahead of the French Open, with top seed and world number five Alexander Zverev also in action on Tuesday, against Ernests Gulbis.
Ugo Humbert was a standout performer at the Lyon Open, ending a three-match losing streak as he beat Cameron Norrie 6-1 6-3, hitting eight aces and converting six of nine break points.
There were no surprises elsewhere, though sixth seed Richard Gasquet had to come from behind to beat qualifier Maxime Janvier 6-7(5-7) 6-2 7-6 (7-2).
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Meanwhile, Tristan Lamasine beat Jannik Sinner to set up a second-round clash with top seed Nikoloz Basilashvili.