Originally Posted by ralfp

This.

However, sometimes the OP's situation could result in an illegal connection (too little time to change flights). I've even had a case where I was rebooked on a later flight such that my connection time became negative (i.e. the 2nd flight left before the 1st flight arrived).

galego may be able to get a refund if the new connection time is too short (depends on the airport, airlines, domestic/international, etc.).