Oh I forgot, another thing I used to do was if was out wiht my husband is ask him to kind of stand/sit in such a way it blocked me from passersby if I was feeling uncomfortable. And before I tossed the cover I had him kind of hold it out for me so it was not resting on babies head which my son hated. Enlisting his help gave us a "we are in this together" type feeling. I think sometimes husbands and other family get perturbed when they see us struggle but they do not know how to help.
And e-bee I understand you were not saying non-covering moms are immodest! But unfortunately moms have occasionally been harassed for nip without a cover, for example a couple years ago a restaurant employee gave a mom a blanket from somewhere (eeeww, first off) and told her to cover up. Not cool!