Starting at the Routeburn Shelter, follow the Routeburn Track as far as Howden Lake. From there continue south to McKellar Hut.
Follow the Caples Track to get back east, to Lake Wakatipu.
Finally, tramp the Greenstone Track until McKellar Hut. Then, instead of retracing your steps to Howden Lake, go west and ascend the ridge, scramble over Point 1543, and follow the main ridge of the Livingston Mountains to Key Summit. Just beyond is the the remainder of the Routeburn Track to The Divide
Each leg can be split up in various ways. The Routeburn Falls Hut was booked out, so I had to adjust by starting with a short day. Hiking for 7 days, I stayed at
1. Routeburn Flats Hut
2. Lake McKenzie Hut
3. McKellar Hut
4. Mid Caples Hut
5. Greenstone Hut
6. McKellar Hut