A scroll compressor for a motor vehicle air-conditioning system includes a compressor housing, two interleaving spirals within the compressor housing, of which one spiral is stationary and the other spiral is movable eccentrically on a circular orbit, whereby the volume of compression chambers formed between the spirals changes cyclically and refrigerant is suctioned in and compressed; at least one refrigerant outlet port for ejecting the compressed refrigerant in a wall, frontal to the spirals, of the compressor housing in the center of the stationary spiral, wherein in the spiral end region on the inner end of at least one of the two spirals the concave side of the spiral wall is provided with a cut that has the form of a cone segment with concave curvature, decreasing from the upper end in the direction toward the lower end of the spiral wall.