The government’s trusted traveler program has proved itself more popular than officials expected, with 1.2 million people now eligible to speed up their entry to this country using a self-service kiosk rather than waiting to speak to a customs agent at the airport.

But some people have been surprised to find that their applications for Global Entry and other trusted traveler programs have been rejected — not for some serious infraction but for a minor brush with law enforcement or customs inspectors that turned up during the required background check.