Aleksandar Vukic has suffered an unexpected defeat to one of Australia's Davis Cup opponents, Tomas Machac, in the Vienna Open, with Alexei Popyrin also departing the ATP 500 event at the first stage.
Those defeats end Australian singles interest in Vienna, although John Peers will play a round-of-16 doubles tie alongside partner Nikola Mektic on Thursday.
At the Swiss Indoors in Basel, Alex de Minaur beat Diego Schwartzman to progress.
Vukic lost 6-3 6-1 to world No.74 Machac - a qualifier in Austria - who will line up for the Czech Republic in the Davis Cup quarter-finals next month.
The match lasted less than an hour, though Vukic - who has climbed to 56 in the world having been ranked 201 in February - was closer than the scoreline suggests.
Broken once in the first set he three times had game point in a 15-minute opener to the second stanza, but thereafter faded.
Popyrin, who like Vukic was overlooked by Lleyton Hewitt for Australia's Davis Cup team, put up a strong fight against No.3 seed Andrey Rublev but was beaten 7-6 (7-5) 6-4.
Stefanos Tsitsipas beat Dominic Thiem 7-6 (7-5) 6-4 and Frances Tiafoe advanced after Dan Evans retired due to a calf injury with the Briton leading 4-1 in the first set.
Grigor Dimitrov, Tommy Paul and Lorenzo Sonego are also in to the second round, beating Lorenzo Musetti, Alexandre Muller and Francisco Cerundolo respectively.
In Switzerland, de Minaur was pushed hard by the battling Schwartzman, taking 105 minutes to defeat the Argentine 6-4 6-4.
The Aussie No.1 broke in a 12-minute opening game, adding a second break to go 4-1 up before Schwartzman broke back.
In the second set, de Minaur broke in the ninth and saved two break points in the 10th before serving out.
He will next face Tallon Griekspoor, of the Netherlands, who overcame Brazil's Thiago Seyboth Wild 7-6 (7-4) 2-6 6-3.
Top seed Holger Rune overcame a 6-1 first set reverse to beat Miomir Kecmanovic 1-6 7-5 6-3 and there were also wins for Nicolas Jarry, Hubert Hurkacz and Dominic Stricker.
Three-time grand slam champion Stan Wawrinka was beaten 6-3 7-6 (10-8) by Russia's Alexander Shevchenko.
