troubled persistently especially with petty annoyances; "harassed working mothers"; "a harried expression"; "her poor pestered father had to endure her constant interruptions"; "the vexed parents of an unruly teenager"
A vexed problem or question is very difficult and causes people a lot of trouble. Ministers have begun work on the vexed issue of economic union Later Mr Moi raised the vexed question of refugees. see also vex = thorny