These are my directions for a short-row heel without wraps. To my knowledge, the copyright for this technique belongs to Coats plc or one of its subsidiaries. This is merely my attempt to explain it better than the pamphlets I have read (in multiple languages).
Like all short-row heels that I have encountered, they are the same knit cuff-down or toe-up.
Instead of wraps, the Boomerang Heel uses "double stitches" (DS). A DS is really just a slipped stitch pulled very tight, as in pull the working yarn over the top of the needle and on around under tight. The legs of the stitch are pulled over the needle, making it look like two stitches, but it is really only one.
If a DS is executed, it is done right after turning the work. If beginning a knit row, the DS is slipped as if to knit (see top photo), then pulled tight. If beginning a purl row, the DS is slipped as if to purl, then pulled tight (see bottom photo).
Although a DS looks like two stitches, it is treated as only one. When knitting or purling into a DS, always treat it as one stitch.
Before you start the heel. . .
Remember that the heel stitches are worked on half of the total stitches in a round. Make sure the half you choose are lined up with the toe (if applicable).
Leave all of the stitches on needles. In the "middle of the heel" section, two full rounds will be knit.
Decide on your heel divisions before you begin. Usually the heel divisions are divided in thirds with any "leftover" stitches going in the middle. For instance, 8/10/8 is recommended over 9/8/9.
The first half of the heel
If you haven't yet done so, knit across the half-round where the heel will be.
*Turn work. Execute a DS (beginning a purl row), and purl to the end of the half round (or to the nearest DS). Do not purl into a DS. They accumulate during this part.
Turn work. Execute a DS (beginning a knit row), and knit to the nearest DS. *
Repeat everything between the asterisks until the desired number of DSs are on each side and the desired number of stitches in the middle remain un-doubled. The last row should be a knit row.
If done correctly, each row is one stitch shorter than the last.
The middle of the heel
Place a stitch marker (A). Knit into all of the DSs on that side. Knit the front of the ankle. Knit the second set of DSs in the back loops. Place a second stitch marker (B). Knit the middle section of the heel in the front loops (should be one full round in total). Knit a second round, stopping at stitch marker A.
The second half of the heel
Remove stitch marker A and knit one more stitch.
Turn work, execute a DS (beginning a purl row) and purl to stitch marker B. Remove stitch marker and purl one more stitch.
*Turn work, execute a DS (beginning a knit row) and knit to the DS, in the DS, and one stitch beyond.
Turn work, execute a DS (beginning a purl row) and knit to the DS, purl the DS in the back loop, and purl (in the front loop) one stitch beyond.*
Repeat between the asterisks until last stitch of the heel half-round has been doubled, ending with a knit row. One DS will remain on the other side of the heel.
Knit in the round, knitting into the DS in the back loop when it comes.
Continue with the instep or cuff of the sock. Enjoy!