If your intent is to learn to carve, I'd recommend against full rocker. And full rocker is not going to help you on ice. I would actually recommend you go a bit wider for more versatility. Head has three options: iSupershape Titan, 80mm, Strong Instinct Ti, 83mm and Monster 83, 83mm. I've skied the first two and own the second one and I also own an 84mm ski, Nordica Fire Arrow 84EDT. The reason I own both is that the Nordica is basically a fat race ski and demands I always have my "A" game engaged when I take them out. They are amazing skis and outrageously fun, when I really want to concentrate. Sometimes I don't feel like doing that and that's why I have the Strong Instinct Ti. It is not as stiff as the Nordica, has a rounded slightly upturned tail, rocker tip, wider tip and tail, shorter turn radius. The Nordica is a handful in bumps and not a lot of fun in more than about 6" of powder, but it has no speed limit that I've been able to find. The Head is not going to feel very stable after probably 50mph, but it's an order of magnitude better in the bumps, handles 6-8" of powder easily, very quick edge to edge and weighs a lot less than the Nordica. It's fun in a lot of different conditions where the Nordica is not. Head claims it's for advanced skiers, but that's nonsense. A ski for advanced skiers is not this easy to ski. The nice thing about it is that the better the input from the skier the better the ski responds. I'm 5'7", 150 pounds and ski the 170. The iSupershape Titan is also a great ski but is for a bit more advanced skier than the Strong Instinct Ti. It's stiffer but will hold better on ice. I've skied it in the trees at Big Sky and was pretty impressed with how well it handled. I haven't skied the Monster 83 but have skied the Monster 88 and liked it.
I would caution you against getting a ski that's only for slightly more advanced skiers because you'll just outgrow it faster. Get something that's a decent step up from what you have so that as your skill improves, the ski will respond better. That's why I like the Strong Instinct Ti, its skinnier sibling the Supreme Instinct Ti and the iSupershape series. See if you can demo one of these, but don't bother with the Natural Instinct or Raw Instinct.