I think it depends on how is the user's body shape and how it is the binder itself.
But I've done many tries and this is what I can tell from my own experience:
-Tight binder (the one you would usually wear during the day): This is my last resort. I would not recommend anyone sleeping in a tight binder since when you sleep, all your body relaxes and well, it expands in some way. I've woke up with painful back, lungs, chest, neck and a horrible numbness.
-Ace bandage: You can try, but if you go as tight as you can you will get 'Tight binder' results. And if you bind a bit more loose your bandages will move and you will end up waking up tied in them and with your breast happily around. (Scary, but has happened to me and it's one beautiful way to say "bad mornings!" from your body)
-Old binder: This is other thing. I have a Underworks shirt that is way too used, it's the double panel kind, and is so used that the only thing that it does is keeping them from moving around and giving you a middle-flat chest. Since its elasticity is quite done, you can breath freely. It's not as comfortable as sleeping just in your pajamas/tshirt/wathever you use to sleep but it can do the trick.
Good luck!