Any tips on making these “baskets” hold their shape?

I have some oddly shaped shelves in my wardrobe and had the bright idea to crochet some baskets for them. They might be too big or I’ve used the wrong yarn because they’re just a floppy mess.

Any ideas on how I can make them hold their shape a bit better? They are going to be very frequently used so I’m wary of starching them given how much I’m going to touch them.