We report the demonstration of single-nanowire photodetectors relying on carrier generation in GaN/AlN QDiscs. Two nanowire samples containing QDiscs of different thicknesses are analyzed and compared to a reference binary n-i-n GaN nanowire sample. The responsivity of a single wire QDisc detector is as high as 2 x 10(3) A/W at lambda = 300 nm at room temperature. We show that the insertion of an axial heterostructure drastically reduces the dark current with respect to the binary nanowires and enhances the photosensitivity factor (i.e., the ratio between the photocurrent and the dark current) up to 5 x 10(2) for an incoming light intensity of 5 mW/cm(2). Photocurrent spectroscopy allows identification of the spectral contribution related to carriers generated within large QDiscs, which lies below the GaN band gap due to the quantum confined Stark effect.