'may' in reported speech

[wace]

Hi everyone
Could somebody tell me if may becomes MIGHT or, preferably, COULD in the following sentence:

Susan: 'May I use your phone, Mr Bradshaw?
Susan asked Mr Bradshaw if she might/could use his phone.

I haven't been able to find a convincing rule in any of the grammar or usage books where I've checked.
Thanks.

[konungursvia]

It is the law of accord of tenses: I think he is right... I thought he was right.

Might is an old past tense of may, just as could is an old past tense for can. So, to change the tense may > might, can > could, to be consistent, although there is little difference in actual outcome.

[wace]

Thank you.
I know there's virtually no difference in terms of meaning. I was just wondering if technically, may should always become might.
I visited an English site a few days ago showing a chart with all the tense transformations and, what do you know, may (permission) becomes could in modern English usage. That's what set me thinking...
Anyway, thanks heaps for your help!