Here's my Asymmetrical Cabled hat with a few changes:
At a certain point (I don't remember how far in, maybe 6"?) I began decreases as follows:
k5 in pattern, k2tog (or p2tog depending on the pattern), to the end
knit one round in pattern
k4 in pattern, k2tog (or p2tog depending on the pattern), to the end
so on and so forth. I tried my best to incorporate my decreases into the pattern. If I came to a spot where I needed to knit a purl together with a knit stitch, I turned that stitch into a knit.
Also, two corrections to the pattern too. The big cable should be twisted on the 8th row and then every 12th thereafter (according to the photo.) And I think it's near impossible to get the gauge on 11's, I'd start swatching with 10's and that's what I used.
I used one skien of Misti Alpaca Chunky which is just the softest yarn EVAR!