Is ab-ab better than a-az?

I believe keeping the rules to aa and abab helps keep it simple and easier to remember.

I agree with the need to keep the number of rules as small as possible. But my question is more whether ab-ab is the best one. The advantage I see with a-az is that you start just as usual, giving all initials - here two. Then you add the z, almost as an afterthought when - and only if - you discover there are too many choices.

But I also shorten abab to aa for very common 2 word phrases

With a-az this does not require a special rule: it just follows from the fact that you start with aa.

Jean Ichbiah