Xavier Malisse and Jarkko Nieminen were among the seeds to reach the second round of the Unicef Open, but Jeremy Chardy lost on Tuesday.
Belgian Malisse, seeded third for the grass court tournament at 's-Hertogenbosch in the Netherlands, made short work of Alejandro Falla, beating the Colombian 6-3 6-1 in just 56 minutes.
World number 41 Malisse lost his serve just once in the match, while breaking Falla five times from 11 opportunities.
Finn Niemen also reached the second round of the joint ATP/WTA event after seeing off Argentine Maximo Gonzalez 7-5 6-1.
Chardy the biggest casualty on Tuesday - the French seventh seed gave away a one-set lead to lose 3-6 6-4 7-6 (9-7) at the hands of American Alex Bogomolov Jr.
In Tuesday's lone second round match, fourth seed Ivan Dodig beat Austrian Andreas Haider-Maurer 6-4 6-3 to reach the last eight of the tournament.
Local hope Robin Haase got off to a good start in front of his home crowd, defeating German Mischa Zverev 6-3 6-4, while Teymuraz Gabashvili beat Spaniard Javier Marti 7-6 (8-6) 6-3.
In other matches, local wildcard Jesse Huta Galung defeated German Julian Reister 6-2 3-6 7-5 and Michael Russell of the United States completed a bad day for the South American contingent, ousting Colombian Santiago Giraldo 7-6 (7-4) 6-3.