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

The sculpture on the early whorls consists of two or three strong cords, swollen where they override the ribs, these are prominent on the periphery.

On the body whorl in front of the keel are about a dozen major threads with wide spirally striate interspaces.

The axial sculpture of (on the body whorl seven) peripheral waves, rather than ribs, overridden by the spirals, the incremental lines inconspicuous.

The outer lip is moderately produced, sharp edged, slightly crenulate by the spiral sculpture, smooth within.