Start at the Lupine meadows trailhead, as for Exum ridge. Follow the excellent trail up Garnet Canyon making sure to stop to admire the wild geologic features on the canyon walls. Hike through the moraine (camping sites here) to the head wall below the Lower Saddle camp. Climb the head wall via a fixed rope or up steep snow to climber's left. From the Lower Saddle hike climber's left, towards Middle Teton.
A note about camping.
If you are planning on climbing this route in two days you will have a couple of choices where to camp, although this may be dictated by permit availability. Installing your camp in the moraine will allow you to descend the Middle Teton glacier from the summit back to camp (non-trival). Camping at the lower saddle will make the approach shorter on summit day, but depending upon your descent route may force you to climb back up the lower saddle from the moraine.
This route has been referred to as the baby sister of the Black Ice Couloir. It is a fine route in its own right, offering engaging route finding and interesting climbing. All in all a great way to climb a classic Tetons peaks. We climbed the route in August and found rewardingly icy conditions and dry rock climbing.
Climber starting up the ridge
From the Lower Saddle first start by climbing the steepening ridge bypassing large gendarmes, first on the left, then on the right. We encountered difficulties to 5.6.
Climbers traversing into the couloir
When able to do so, traverse climber's right into the broad gulley above a vertical cliff on loose, sloping ledges. This traverse to the hanging gulley was for us the sketchiest part of the route.
Climber on the first pitch in the couloir
Establish a belay (pitons helpful here). Once in the couloir proper the route is straight foward. Climb four 60 meter pitches of snow/ice to 70 degrees (at the very steepest). Ice screws, pickets and rock gear were all useful for protection and belay anchors. At the top of the couloir may be a cornice, which for us was the steepest section. Pull the cornice then scramble easy terrain climbers left to the summit. The summit affords oustanding views, particularly of the entire Direct Exum Ridge.
Middle Teton glacier
Perhaps the most least technical descent is to follow the Middle Teton Glacier route back to the moraine. We found this to be not entirely trival. We made several rappels from fixed anchors down a rock chimney and found steepish snow and ice to 45 degrees.
Helmet, rope, 4-5 ice screws, 2 pickets, 6-8 slings, carabiners, crampons, two ice tools, small rock rack including 6 nuts and cams from .5" to 1". We found pitons to be useful as well.