You shouldn't use one for your postpartum bleeding, just like you shouldn't use a tampon. Honestly, you will NOT want to. I hated pads and never, ever used them before I had my daughter. But now I actually prefer them because the moon cup/tampons are not as comfortable as they used to be. I didn't even get my period for about 5 months after birth and even then it was still a bit uncomfortable to use one. You may also need to go up a size in the moon cup (to the one for women who've given birth, if this is your first baby and you now use the smaller size). But really, once your lochia bleeding stops and you get your first real period, you can safely use a moon cup or tampons again, assuming everything is healed if you had a tear.