Some self-styled sticklers I know, perhaps still smarting at the " 'May' is for permission" lecture they got when they asked "Can I go to the bathroom?" in first grade, insist on changing "may" to "might" whenever they see it used in a non-permission sense. That can be fine -- "I might go to the party" may/might indeed be better than "I may go to the party" -- but it can also screw things up.
Be especially careful when the word "have" is involved. Observe:
"She may have been killed."
"Oh, dear. I hope she just got lost and we hear from her soon."
"She might have been killed."
"So true. Thank goodness she was wearing her seat belt."
(If you read the former example as a quote from a mob boss giving instructions to a hit man, proper English usage is the least of your problems.)