Okay, I've been looking at the hat so far, and I've realized that my problem with doing p1k1p1k1p1k1 is that it will screw up the look of the hat.
The patter for the body of the hat is:
Rnd 1: P1, (K1, P1) around.
Rnd 2: K1, (P1, K1) around.
Repeat Rnds 1 and 2 for patter until piece measures approximately 5 1/2" (14 cm) from cast on edge, ending by working Rnd 2.
The result is purls on top of knits for every round, making it look really bumpy.
Anyway, I know if I did p1k1p1k1p1k1 it would result with knits on knits and purls on purls, like ribbing. I know because there are a few areas where I've done that by mistake, and it doesn't look right.
So I tried the other method, knitting and purling into one stitch and that was weird, too, because it added six more stitches when, at this point in the pattern, I'm supposed to start decreasing stitches (going from 111 sts to 89).
Maybe, I wasn't doing it right? It just didn't seem right to have added more stitches. Not to mention it was twisting weird, even though I tried to make sure that I was moving the yarn for every knit and purl.
I hope I'm being detailed enough. Actually, I think I could be leaving out something. When/If it comes to me, whatever it is, I'll add it asap.