Twists, etc

Recently, I was reading a German sock pattern and saw directions for making left and right twists (2 stitch cables). I immediately thought: This is so obvious. Why haven't I seen anything like this before?

My German isn't that good. This is what I think I read:
(Well, after the translation came out, I discovered that I had misread second for two , and the directions are for the usual pinch method of cabling without a cable needle. But, the following directions do work.)

For a right twist: Put the RHN (right hand needle) into the first 2 stitches of the LHN (left hand needle) as if working a k2tog. Slip the 2 sts off the LHN but do not knit them. Slip them back onto the LHN purlwise. The sts are twisted with the st nearest the tip of the LHN lying over the next st. Knit the first st tbl (through the back loop). Knit (or purl) the next st tbl. (Purl the second stitch if you want a right twist with purl back. Otherwise knit it.)

For a left twist: Just as the right twist starts out as if one were making a k2tog, the left twist starts out as if one were making a ssk -- or more accurately a ssp. Reposition the first 2 sts on the LHN needle as if working a ssk or ssp. (In other words, slip the 2 sts to the RHN individually knitwise. Then slip them back to the LHN purlwise.) Slip the RHN into the back of the 2 sts on the LHN as if working a ssp. Slip them off the LHN but do not purl them. Slip them back onto the LHN purlwise. Knit (or purl) the first st. (Purl the first stitch if you want a right twist with purl back. Otherwise knit it.) Knit the second st.

For a left twist (with fewer steps): Slip the first 2 sts on the LHN individually to the RHN. With the points of both needle facing the same direction and the LHN in front of the RHN, place the LHN into the 2 sts and slip them off the RHN. Knit (or purl) the first st. Knit the second st.

Now to decreases and increases....
After reading about making centered double decreases instead of paired single decreases for shaping sleeves, etc. in Knitting Daily, I've found that I like them a lot. I use Fleegle's method of making a centered double decrease. But, instead of working the stitch in one step as she does, I first slip the 1st 2 sts on the LHN to the RHN together knitwise. Then slip the next st on the LHN to the RHN knitwise. Finally, knit the 3 sts together through the back loop. This leaves a ridge in the center (equivalent to s2kp or cdd). On the other hand for a centered double decrease that looks like a sk2p, slip 1 st knitwise from the LHN to the RHN. Then slip the next 2 sts together from the LHN to the RHN knitwise. Finally, knit the 3 sts together through the back loop. (These have the added advantage, at least for me, of being easier to frog than the "pass st over" methods.)

I wasn't able to find anything on centered p3tog's. So, here's how I ended up making some in order to have the stitch look like a centered k3tog from the wrong side:
Leave the yarn in front. Turn the knitting over so that the yarn is now in back. What was the RHN is now the LHN and vice versa. Slip the 1st 2 sts on the LHN to the RHN together knitwise. Then slip them back to the LHN purlwise before finally knitting 3 sts together through the back loop. Slip this st back to the LHN knitwise. Turn the work over. The stitch is complete.

Finally, to get a centered double increase to match the centered double decrease (for shaping). In the same stitch, p1, yo, p1.

Here's a link for an interesting and, at least for heavier weight yarns, better, way to make a double increase. And since sometimes links disappear, here is a brief summary: k1tbl, k1 in same st. Place vertical bar of st just knit onto LHN. k1. You get a nice single increase by just working the first part of the stitch (k1tbl, k1 in same st).