A compressor for a turbine engine, including: a casing, at least one compressor stage including an impeller having stationary blades and an impeller having moving blades positioned downstream of the stationary blade impeller, and cavities in a thickness of the casing that are disposed along a circumference of the casing opposite the moving blades. The cavities, which are elongate and extend along a main direction of orientation, are closed upstream and downstream by upstream and downstream faces respectively, and an upstream border and a downstream border are formed at the intersections between same and the casing. The cavities are offset in relation to the moving blades to overlap the moving blade impeller in the upstream portion, thereby covering the upstream end thereof. The downstream border of the cavities is oriented parallel to the chord at the head of the moving blade.