Supraglacial debris is known to strongly influence the distribution of glacier surface melt. Since melt inputs drive the formation and evolution of glacial drainage systems, it should follow that the drainage systems of debris-covered glaciers will differ from those of debris-free glaciers. This would have implications for the proglacial runoff regime, subglacial erosion and glacier dynamics. This paper presents analysis of return curves from 33 successful dye injections into the extensively debris-covered Miage Glacier, Italian Alps. It demonstrates that the spatial distribution of supraglacial debris influences the structure and seasonal evolution of the glacial drainage system. Where the debris cover is continuous, melt is lower and the surface topography is chaotic, with many small supraglacial catchments. These factors result in an inefficient englacial/subglacial drainage network beneath continuous debris, which drains to the conduit system emanating from the upper ablation zone. Melt rates are high in areas of clean and dirty ice above the continuous debris. Runoff from these areas is concentrated by inter-moraine troughs into large supraglacial streams, which encourages the early-season development of an efficient englacial/subglacial conduit system downstream of this area. Drainage efficiency from the debris-covered area increases over the melt season but dye-trace transit velocity remains lower than from moulins on the upper glacier. Future runoff models should account for the influence of supraglacial debris on the hydrological system.