Shell very small, resembling Obtusella (Rissoidae), bluntly conical, perfectly transparent, vitreous but not very glossy. Protoconch with 0.6 whorls, diameter 220 µm , sculptured with numerous small granules, more crowded at nucleus. Teleoconch with up to 2.4 strongly convex whorls with very deep suture. Initial 0.5 teleoconch whorl sculptured by very short anastomosing, crossing and branching, axial and spiral riblets. Riblets on last 1.5 whorls predominantly spirally oriented and mostly branching. Intermediate part of teleoconch with transitional sculpture. Similar, though more crowded, sculpture in narrow, deep umbilicus. Aperture orthocline, radial, perfectly round, in contact with preceding whorl for very short distance.
Dimensions. Height of holotype 1.06 mm, diameter 0.91 mm, height of aperture 0.52 mm, breadth 0.52 mm. Operculum: very thin, transparent, coiling hardly perceptible.
Radula. 4-2-1-2-4. Central tooth with one main and three smaller lateral cusps, and strong lateral supports. First lateral tooth broadly triangular with a small cusp. Second lateral tooth tall and claw-shaped with two outer and a single inner cusp in addition to apical main cusp. Marginal teeth 1/3 of width of outer lateral, with two small denticles on outside of main cusp, bases slightly expanded longitudinally.
Anekes undulisculpta differs from A. sculpturata by having about 0.4 whorls less at a comparable size. At 0.85 mm height A. sculpturata has 2.4-2.5 teleoconch whorls, A. undulisculpta has 2.0-2.1 whorls. The sculpture of the first teleoconch whorl at A. undulisculpta is mainly spirally oriented, while in A. sculpturata it is very irregular. Furthermore, the radulae are quite different.

Type material Holotype and 2 para types in MNHN, 1 paratype SMNH 3656. Type locality. Southeastern Bay of Biscay, 44°36'N, 02°08'W, 230-330 m.
Material examined. The types and —southeastern France, off Banyuls, Rech Lacaze, 270-254 m, 10 shells, SMNH; — southeastern Bay of Biscay, 44000'N, 02°lO'W, 280-300 m, 1 specimen, MNHN.