Understanding the future evolution of Himalayan glaciers is important in terms of runoff that provides an essential water source to local populations and has far-reaching downstream impacts. However, the climatic response of glaciers in High-Mountain Asia is complicated by ice stagnation and considerable supraglacial debris coverage, which insulates the ice from warming. Typical runoff modelling only crudely incorporates debris cover and there is currently no consensus on how significantly this may impact future glacier and runoff evolution. Here, a glacio-hydrological model is modified to incorporate fully distributed debris cover, using melt reduction factors that vary depending on debris thickness, and to redistribute mass losses according to observed surface elevation changes. A range of debris thickness data are implemented, including a remote-sensing survey and a modelled debris surface, to analyse the sensitivity of glacier evolution and runoff to possible future debris-cover changes in a series of experiments in the upper Khumbu catchment, Nepal. Simulations are undertaken using climate input data from Regional Climate Model simulations from CORDEX (Coordinated Regional Downscaling Experiment) which are further statistically downscaled using data from the Pyramid meteorological station. Results suggest that the accurate calibration of the model to volume change compensates for the inclusion of distributed debris cover but only if the climatic sensitivity of the calibration period (1999–2010) and the nature of the debris-covered surface remain constant during future simulations. Altering the nature of the debris surface has a significant impact on simulated ice volume, with melt rates under debris suppressed by up to 85 %. The sensitivity of runoff ranges from 60 to 140 million m³ yr^-1, although there are considerable uncertainties relating to non-glacial snow melt. Moreover, incorporating locally enhanced melt at ice cliffs into the model also impacts upon volume loss and discharge, with a greater proportion of ice cliffs leading to enhanced volume losses compared to a homogeneous debris surface. Finally, using the most representative model configuration, the future evolution of Khumbu Glacier under various climate scenarios shows continued mass losses with a reduction in volume ranging from 60 % to 97 % by 2100. Runoff trends show an initial increase followed by an eventual decrease, with runoff in 2100 predicted to be 8 % lower than current levels.