In this first teshuva in Igrot Moshe, Rav Moshe Feinstein was asked if one is permitted to walk around with his head only partially covered, i.e. if he is wearing a small kippa.
Interestingly, Rav Feinstein does not attempt to define how much of the head is too much or too little (at what point in the slope downward of the head does one no longer need to cover it?). However, he cites the view of Rav Shlomo Kluger who states that one can walk fewer than four amot with the head partially covered and not at all if the head is uncovered. Rav Feinstein's analysis then demonstrates that Rav Kluger seems to have an extreme view on this point, and that the wearing of a kippa is largely a מדת חסידות, although nowadays it has been accepted by Jews as a requirement for everyone. Rav Feinstein concludes that given its near-universal acceptance, one should not even sit without wearing a kippa, as there may be a חוקות עכו"ם problem (although it is not completely clear what practice of the non-Jews this would be emulating).