Having a head covering on long hair is much better than not covering at all
Same for covering only at shul:
Encyclopedie Talmudique, vol VIII page 24 "dat moche"
Having a tefach (8 to 12 cms) showing : R’ Feinstein (iggerot Moche Orakh Khayim livre 4 responsa 112, par. 4), R’ Aviner
The person looking at you cannot see a ‘full’ tefach in one
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