I don't use a cover, but I wear nursing camis and a looser shirt over, and just use DD's head to cover if we're in public. Sometimes if I have a lightweight blanket handy, I will pull the corner of it up to and a little past where DD's mouth is, so none of my skin is showing. I don't believe anyone has ever spotted my nipples in public. Some of my shirts work really well, and I have carried DD around Walmart while nursing and no one could tell. It just looked like she was asleep. If I'm with other nursing moms, I don't work as hard covering, but I still don't let it all hang out, though several of them do. I think some of the people at my church think I'm a little odd for BF in public when other moms bring bottles, but I really don't care. My DD is so healthy, almost never gets sick, and is extremely happy and relaxed all the time. I have had friends comment on how they like that DD is always in my arms instead of in a carseat on the floor, and on how she never fusses in public.
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