Leave the hut and get back onto the Übeltalferner Glacier. Cross this briefly to reach the east ridge of the Wilder Pfaff. Climb the ridge, which is continually interesting but never hard (roughly grade 2 scrambling) and it takes around 2 hours to climb it from the hut. Descend easily down the Sulzenauferner Glacier from the summit and then swing around and climb up to the foot of Zuckerhütl's east ridge.

Following red paint marks, scramble up to the summit, initially on the east ridge and then, as you get closer to the top, on the south face, to the summit. The final scramble is never "difficult" but it is exposed at times and the rock quality is not always great. It is “only” grade 2 scrambling but it can feel intimidating and you might be glad of a rope.

From the summit, take in the extraordinary views, pat yourself on the back for having reached the highest summit in the Stubai valley and then descend back to the glacier. Cross the Sulzenauferner west-northwest to reach the Pfaffenjoch Col. Carry on westwards down the Pfaffenferner Glacier and then across a stream (there's a bridge, fear not) to reach the Hildesheimer Hütte. Grab a drink and get ready for a final bit of effort in getting up to the Stubai Gletscher cable car. (N.B. Years ago it was possible to descend the Sulzenauferner Glacier and then cross the Beiljoch Col to reach the Dresdner Hütte in the middle of Stubai Gletscher ski area, but this is now impossible as glacial retreat has made the toe of the Sulzenauferner Glacier very dangerous and prone to rockfall.)

From the hut, climb up for just over an hour to reach the top of the cable car at the Stubai Gletscher area. Ride this down in triumph and make your way back to Innsbruck using the excellent bus system. Or, if you're really keen, only go as far as Neustift and then bag more Stubai summits in the coming days!