My last time in Rome, a bancomat gave me a couple of 100-Euro notes. I went into the bank itself, explained to the banker (in Italian) that I wanted to get 20-Euro notes, instead, and he refused. He said that the bank didn't exchange money, even though I clarified that I didn't want foreign exchange, just Euro-for-Euros that I'd withdrawn from their bancomat. On the other hand, I've had other banks willing to make this type of exchange. I just wouldn't count on it.