Totally Tubular, plus a review of grafting

I just learned the absolute best technique for casting on and binding off 1x1 ribbing: tubular cast-on and tubular bind-off. When complete, they look almost exactly the same, and they give the ribbed edges of the knit piece a smooth, rounded finish. Here are some brief instructions:

Tubular Cast-On

Picking up stitches for a tubular cast-on. Lighter color
is waste yarn; darker color is working yarn.

Using contrasting waste yarn, cast on 1/2 the number of stitches you will want for your ribbing. Knit 1 row or round. Cut the waste yarn, leaving a 6 inch tail. 
 
Join pattern yarn and work 2 rows or rounds of Reverse Stockinette Stitch. On next rnd, *purl 1, then slip purl bump from first row or round of pattern yarn onto needle and knit this st. * Repeat from * to * until all stitches and purl bumps have been worked. (See diagram.) The number of stitches is now double the cast-on. From this point, work P1, K1 ribbing to desired length. After a few rows are complete, carefully remove waste yarn.

Tubular Bind-Off

You will need two empty needles for this step. Circular are best; it doesn't matter if they are slightly different sizes, as long as they are close to the size of the working needle.

Beginning with a purl stitch, work P1, K1 ribbing to desired length. When final row or round of ribbing is complete, divide stitches as follows: Hold both needles together in your right hand with tips facing left. *Slip first stitch (purl) onto one needle and hold in back; slip next st (knit) onto other needle and hold in front.* Rep from * to * until all stitches are divided. All purl stitches should be on the back needle; all knit stitches should be on the front needle. Break yarn, leaving a tail at least 3 times the length of your bind-off row / round. If you used straight needles, slip stitches onto a new needle so the yarn tail is at the working tip; if you used circular needles, slide stitches so tail is at the right tip. Graft stitches using Kitchener stitch, exactly as you would for a sock. Don't worry about the ribbing - it doesn't affect the way the stitches are grafted.

Grafting: a Quick Review

Here are the steps for grafting (aka Kitchener Stitch). When you're grafting stockinette or 1x1 ribbing, it helps to remember that on the side facing you (the front needle) you see the knit side of the stitches. On the side facing away (the back needle), you see the purl side of the stitches. So when you're completing a stitch, you'll be doing so knitwise on the front needle and purlwise on the back needle.

Begin by cutting your yarn, leaving a tail at least three times as long as your bind-off row. Thread it through a yarn needle and repeat the following 4 steps until all the stitches are gone off your needles:

1. Back needle: Draw yarn through first stitch purlwise, slip off needle.
2. Back needle: Draw yarn through second stitch knitwise, leave on needle.
3. Front needle: Draw yarn through first stitch knitwise, slip off needle.
4. Front needle: Draw yarn through second stitch purlwise, leave on needle.

Periodically use your needle or a crochet hook to adjust the completed stitches, making sure they are even.
This is the memory aid I repeat as I graft:

Back: Purl 1 off, knit 1 on; Front: Knit 1 off, purl 1 on.