It's easy to pack 9 days' worth of clothes in just a carry-on. I think the reason people tend to overpack is because they see their trip/vacation as a fashion show: a new outfit for everyday with matching shoes and handbags. When I travel, I wear what I usually wear at home.
It's a matter of planning. I have done it for so long that it's just second nature to me now. For a 9 day trip I pack 2 pairs of jeans (darker colors can be dressed up), a pair or two of nice slim trousers or skirt for the dressier occasions, 3 t-shirts (you can also buy more at your destination), 2 fine wool sweaters/cardigans, 2 more tops, enough underwear for everyday + at least two days extra. I pack dressy shoes that I can walk in (usually my black Chanel wedges) and I wear my coat on the plane with another sweater/cardigan. I bring an everyday purse and a small clutch. I also make sure all bottoms work with the shoes (i.e. don't bring trousers that are too long for flats). If I have to, I send out clothes to get laundered.
My facial regimen is not involved therefore doesn't require me bringing an entire make-up counter, and my hair is not so needy as to require a full size shampoo and conditioner. In fact, I like buying and trying local products - I've found some really great stuff; the only time this backfired on me was in Cambodia where all the lotions had bleaching agent in it; I bring body lotion with me all the time now. I don't bother bringing a hair dryer because they won't work; besides, any decent hotel will have one.
It's mostly common sense, really.