Dispersion control with axially nonuniform photonic crystal fibers (PCFs) permits supercontinuum (SC) generation into the deep-blue from an ytterbium pump laser. In this Letter, we exploit the full degrees of freedom afforded by PCFs to fabricate a fiber with longitudinally increasing air-fill fraction and decreasing diameter directly on the draw-tower. We demonstrate SC generation extending down to 375 nm in one such monolithic fiber device that is single-mode at 1064 nm at the input end.