Shell small, white, moderately solid, depressed, widely umbilicate. Whorls 3,25, including a smooth low convex protoconch of 1,5 whorls. Surface of post-nuclear whorls crowded with extremely fine and dense spiral striae. From the umbilicus, which is about one-fifth the major diameter of the base, there are twenty-five strong radial folds. These are strongest at a little distance out from the edge of the umbilicus and fade out entirely at about half way towards the periphery. Spire low, less than half the height of the aperture. Whorls evenly rounded. Aperture circular. Peristome continuous, slightly thickened and actually detached from the parietal wall. A faint spiral joins the lower part of the inner lip.
Height 1,05 mm.; major diameter 1,45 mm. (Holotype).

This species bears an extraordinary resemblance to Argalista rotella, n.sp., described herein from the same dredge station. Shape, size, umbilicus and basal radial folds are closely similar in both species, but paradoxa has the characteristic continuous peristome of Cirsonella and dense microscopic spiral striations, while rotella has a discontinuous peristome with a thin edge, overhanging above as typical of Argalista, as well as fewer and stronger spiral striations.

Habitat: Off Three Kings Islands, St. 933, 260 m.