Compsodrillia thestia is a species of sea snail, a marine gastropod mollusk in the family Pseudomelatomidae, the turrids and allies.

(Original description) The slender, acute shell is strongly sculptured, with pale brownish clouding on a yellowish white ground.

Other spiral sculpture consists of (on the spire one or two) strong peripheral cords, swollen and almost angulated where they override the ribs.

On the body whorl there are six or seven cords with much wider interspaces and as many more smaller close-set threads on the siphonal canal.

[2] This marine species occurs in the Sea of Cortez, Western Mexico.