In 1986, Rüedi was the first Swiss, along with Peter Habeler, to summit Cho Oyu. That same year, he and Krzysztof Wielicki attempted to climb Makalu via a standard route variation. Wielicki reached the summit a few hours before Rüedi and was able to descend to the nearest bivouac shelter. Rüedi did not succeed. Reinhold Messner, who was also at Makalu at the time, claims to have seen Rüedi descending from the summit, and watched as he disappeared behind a snowdrift. Messner later found Rüedi sitting dead in the snow just below his camp.