Publicity surrounding heartless wise man had improved (11)

I haven't cracked this one yet — but the brilliant team at Times for the Times have:

Publicity here is AD (not PR) which you put around a wise man without its middle. No, not a sage, or a guru, nor even a magi in its generic sense but specifically MELCHIOR without his middle two letters. You then have to add ATE for “had”. Difficult w/p so if the correct synonym for “improved” immediately jumped out at you, you did better on this clue than me!