The Petite Dent de Veisivi Traverse from the Col de Tsarmine over the SE Ridge, also called the Tsarmine Arête, with descent over the SW Ridge is definitely the most rewarding climb on this mountain. The ridge consists of 4 gendarmes, which all have to be climbed more or less directly. Overall difficulties are UIAA II/III with some moves of IV in the crux on the Grand Gendarme. Pleasant climbing on sound rock will guarantee a nice trip.
The route is described in Valais Alp West
Selected Climbs by Lindsay Griffin.
From Satarma cross the bridge on the other side of the road and start walking in northern direction. Immediately after a small bridge turn right and start following a marked track (red on white flashes) to the Col de Tsarmine. The track first rises steeply through the forest, then passes left below the Tsarmine shepherds' huts and climbs on grassy slopes below the Petite Dent de Veisivi. Finally the Col de Tsarmine is reached on rocky slabs (some cairns).
The track is well indicated on map 1327 (Evolène).
Several guidebooks warn for a long and strenuous approach to the Col de Tsarmine. Indeed the first part of the approach is quite steep, but fit parties will not have any problems to complete the approach within the timeframe indicated by the guidebooks.
From the Col de Tsarmine, head in northern direction on easy rocks (scrambling), staying on the crest of the ridge. Gradually the ridge becomes narrower and more exposed. The first gendarme is traversed easily and also the second gendarme is climbed directly (III). The third gendarme, also known as the Grand Gendarme, offers the crux of the route (IV). Climb a short slab (1 spit, 1 piton) into a chimney and continu up right until you reach a small ledge where you can make a belay on a sling. Continu straight up to the summit of the third gendarme (one spit slightly on the left). It might be tempting to climb from the ledge right around the corner, but this will get you off the route. A short rappel from the third gendarme leads to a small step which can be turned on the right (III). More easy terrain now leads to the top of the fourth gendarme. Another very short rappel and easy but exposed scrambling leads to the gap between the fourth gendarm and the summit. From here easy scrambling on wonderfull rock leads to the summit of the Petite Dent de Veisivi.
Descent via the SW Ridge (normal route) is technically quite easy, however, things can become steeper and more difficult if you get off the route. It is possible to rappel down the ridge (good belays in place), but it is probably quicker to down climb, thereby using the belays for protection. When you reach a small saddle, follow a steep track to the left until you are back on the approach route.
A small rack with some friends, slings and quick draws will do. Don't forget that it's an alpine rock climb and weather conditions can change quickly, so carry a raincover and warm clothes with you.