A compressor stage comprising a pair of bladed discs spaced apart from one another having a plurality of bleed tubes located in the space between the bladed discs. Each bleed tube has an internal and an external surface extending radially from an inter-disc cavity at the radially innermost section of the tube to a rim of the bladed discs at radially outermost section of the tube. The bleed tubes are positioned between the bladed discs, such that the bleed tubes remove a portion of air passing through the compressor stage and direct it to an area within the inter-disc spacing. The geometric shape of the internal bore of each of the bleed tubes changes along its lengths. The cross-section of each of the bleed tubes may have a cross sectional area that changes from a substantially non-polygonal shape at the radially outermost end to a substantially polygonal shape at the radially innermost end.