In our case, the postal code (Canadian) and almost any other piece of data is uniquely identifiable. Through a quirk in the layout of our street, my wife and I have the only house in our postal code. Add age, gender, birth month, hair colour, t-shirt size... pretty much anything, and you’ve reduced from 2 possibilities to 1.

I still want to try dropping a letter in a mailbox from a different city with just our postal code written on it and see if it arrives.

It's impossible to anonymize some data. If you're including demographics and locations then yeah, it's going to be hard or impossible to anonymize. If you're using surveys on emotional state or perhaps newsgroup comments? That's not so hard.