To allay something is to make it less or get rid of it altogether: She allayed my fears by saying that she also had heard nothing; I want to allay any doubts you may have about this. To alleviate is to relieve something unpleasant or painful by making it less severe: The ointment soon alleviated the discomfort; Volunteer workers did their best to alleviate the situation. To assuage is similar, but is mainly used of unpleasant emotions or bodily sensations: I tried to assuage the old man's terror; The crew were desperate to assuage their fearful thirst.