* Double medal joy for Switzerland with gold and bronze
* Shiffrin settles for silver to go with her giant slalom gold
* Vonn fails to complete slalom after grabbing first leg lead (Adds detail, quotes throughout)
By Simon Evans
PYEONGCHANG, South Korea, Feb 22 (Reuters) - Switzerland's Michelle Gisin held off the might of American Alpine skiing to win the women's combined at the Pyeongchang Games on Thursday, claiming victory ahead of Mikaela Shiffrin while her fellow Swiss Wendy Holdener won bronze.
Shiffrin's American compatriot Lindsey Vonn, who had led after the downhill section, was the last skier to compete but was unable to finish her slalom run, leaving the 24-year-old Gisin to savour her first Olympic medal.
Gisin's victory, with her combined time of two minutes, 20.90 nearly a second ahead of pre-race favourite Shiffrin, completed a rare Olympic double for her family after elder sister Dominique won the downhill in Sochi four years ago.
"It's so exciting. It's insane I really thought it's so hard to ski so fast in slalom," Gisin told reporters.
"I tried to give it my all and to put my whole heart in that run and I knew I had to be fast to keep a little distance because with Lindsey, you never know how fast she skis in slalom because she was amazing a couple years ago.
"I was scared while skiing because this season slalom kicked my butt so many times... I was believing that one day I will put all the pieces together, one day it will all come to me and today it was exactly that," the Swiss added.
The two medals take Switzerland's tally to six in Alpine skiing at these Games, their most in a single Winter Games since 1988, when they won 11.
Shiffrin departs South Korea with two medals after she won gold in giant slalom and despite wild pre-Olympic predictions of her sweeping every event she entered, the American was satisfied with her return.
"I came into these Olympics knowing I could be a medal threat in multiple disciplines. I didn't even know how many I would ski," she said.
"After the gold in the giant slalom, I was really hopeful and positive. Then I had a tougher day in the slalom (she finished fourth) but it still feels good though."
Holdener produced the fastest slalom run of the day with a 40.23 and held on to bronze, with Norwegian Ragnhild Mowinckel struggling in the technical element and then Vonn skiing out early in her effort.
For Holdener it was a second medal of these Games following a silver in slalom.
"The slope wasn't that good anymore, it wasn't that smooth so in the end I thought it was going to be fourth place. I'm really happy it was enough for the third place," she said.
The joy was particularly sweet given that she was able to share success with her compatriot Gisin.
"It's a really cool moment because we are friends and grew up together. It's amazing," she added. (Reporting by Simon Evans and Rory Carroll; Editing by John O'Brien)