Drapes about the head of the basinet are not only often in the way, shutting out air, etc., but they also gather dust and are unsanitary.
"The Mother and Her Child" by William S. Sadler
BASINET (a diminutive of "basin"), a form of helmet or headpiece.
"Encyclopaedia Britannica, 11th Edition, Volume 3, Part 1, Slice 3" by Various
His helmet is a basinet, pointed at the top, probably worn over a complete hood of mail flowing to the mid-breast.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 6" by Various