Is it mandatory to put a return address on a package?

I need to send a package from Canada to the USA. I don't feel comfortable putting a return address on since i don't really know the people. To send by normal mail (bringing it into the post office), will they make me put a return address on it? I know that if it gets lost/undeliverable that I won't be able to get it back, but that'll be ok. But do you know of a way to make sure that it will be deliverable for sure. What makes it undeliverable?
Thanks in advance!