Lewis & Short

quăsillum, i, n., and quăsillus, i, m. dim. [qualum], a small basket for various purposes; esp., a wool-basket (class.), Cato, R. R. 133.
Of wool-baskets: inter quasilla pendebatur aurum, in the spinning-room, Cic. Phil. 3, 4, 10: pressumque quasillo Scortum, who must spin, i. e. low, mean, Tib. 4, 10, 3; Prop. 4 (5), 7, 37.