What's the difference between "may" and "might"?
He may be right.
He might be right.
Both imply possibility, but "might" is used when the probability is much lower.

Hope this helps! Emotion: smile
The above being true, 'might' is actually the past tense and also the subjunctive form of 'may', although it is slowly losing this identity nowadays and is used mostly as described above.
Still, careful writers will not use 'may' when referring to the past or when the subjunctive needs be used.

'You might have been more credible if...' sounds and is indeed more natural than
'You may have been more credible if...'