Finish this sentence..."When a woman doubts that a man is well sought after, ..." ?

she'll wonder why he's hiding his light"

Well sought after? I don't think that's right but i'll finish the sentence.
It means that she's much cooler than him and he won't break up with her because of the fact she's cooler than he is

Sorry, I don't know what "well sought after" would mean. In fact, I don't believe "well" is a possible adverb to modify "sought after".