The base cover is a problem because of the big plastic circle, but I put the column cover inside the big cover, roll them up tight, like a bedroll, and bungee with two bungee cords and the whole thing fits on the top shelf of a shallow bedroom closet, but just barely. I stand the base cover up on one edge behind the stuff in the bottom part of the closet.
But then I don’t use the whole set very often. For the harp I moved all the time I just kept the main cover draped over the carrier when I put that away.