I am interested in knowing what words/phrase/idioms I can use to express a double reversal of decision.

To illustrate that with an hypothetical example to clear any confusion that may have risen :

I had the idea of buying a phone for someone, decided against it, and then thought about it a bit more and ultimately chose to do it.

What do you think about saying "I changed my mind, and then I changed my mind back." in that context?