untroubled -- (not beset by troubles or disturbance or distress; "seemed untroubled by doubts of any kind"; "untroubled sleep"; "a kind untroubled face")
secure, unafraid, untroubled -- (free from fear or doubt; easy in mind; "he was secure that nothing will be held against him")
untroubled -- (free from turmoil or worries; "untroubled times")