What are the main morphological factors that control the heterogeneous responses of debris-covered glaciers to climate change in the southern central Himalaya? A debate is open whether thinning rates on debris-covered glaciers are comparable to those of debris-free ones. Previous studies have adopted a deterministic approach, which is indispensable, but is also limiting in that only a few glaciers can be monitored. In this context, we propose a statistical analysis based on a wider glacier population as a complement to these deterministic studies. We analysed 28 glaciers situated on the southern slopes of Mt. Everest in the central southern Himalaya during the period 1992–2008. This study combined data compiled by three distinct studies for a common period and population of glaciers for use in a robust statistical analysis. Generally, surface gradient was the main morphological factor controlling the features and responses of the glaciers to climate change. In particular, the key points that emerged are as follows. 1) Reduced downstream surface gradient is responsible for increased glacier thinning. 2) The development of supraglacial ponds is a further controlling factor of glacier thinning: where supraglacial ponds develop, the glaciers register further surface lowering. 3) Debris coverage and thickness index were not found to be significantly responsible for the development of supraglacial ponds, changes in elevation, or shifts in snow line altitude. •Downstream surface gradient is the main factor controlling changes in mass balance, surface, SLA, pond density.•Reduced downstream surface gradient is responsible for increased glacier thinning.•Where supraglacial ponds develop the glaciers register further glacier thinning.•Debris coverage and thickness were not found significantly responsible for changes in glacier elevation.