Wrap Storage and Transportation Ideas?

How do you deal with bringing your wrap or carrier with you somewhere?

A base +3 woven wrap is what's most comfortable for me, but that's a massive amount of fabric to carry around. Even the bei dai I have from my SIL came in its own little carry bag because the straps are so long.

I'm mostly asking what other people do for taking their wraps with them on outings, but I'm also curious about how you put it away at home.