Sock Construction
When I first started making socks, I did it the Dutch way, meaning...

... cuff-down, heel flap knit back and forth, short-row cup, with stitches picked up along the flap and cup for the gusset. Sometimes I would knit a small intarsia design on the heel flap, but more often I would use a reinforcing heel stitch like eye of partridge. This is the method I used to make the socks in my last post.

I once tried what some designers refer to as the eastern method, which is knit cuff-down, with waste yarn used where the heel would be. When you get to where you would normally start the heel flap, you knit those stitches using waste yarn, slip them back to the left-hand needle, and knit them again using the good yarn. Then you do the foot and toe, which are finished in the normal way. The waste yarn is snipped out and the heel is knitted with the live stitches in the same manner as the toe.

I'm not fond of this method of construction, as leaving the heel for last means that you can't try on the sock as you go along. Also, it means using two pieces of yarn per sock instead of one continuous piece, and that means more ends to weave in.
For a while I used the Strong heel, which is named after the designer, Gerdine Crawford-Strong. It was described in the Fall 2003 Knitter's Magazine. You knit the sock cuff-down, and when you get to the heel, you increase the stitches to make the gusset. In the diagram below, the pink outline shows the area that a dutch heel flap would cover. The green dots on the leg show the increases that make the gusset.

The bottom cup of the heel is short-rowed, and the foot and toe are completed as usual.
Perhaps you can see the Strong heel in these slippers.

I eventually abandoned the Strong heel because it proved too fussy to reinforce the heel using a textured pattern.
Today, I started a pair of toe-up socks. To simplify things, which for me equals minimizing seams, instead of a provisional cast-on, I started with a regular cast-on but did double-knitting (the same method used for starting the head of my One-Seam Bear).
A toe-up sock means I have to do a short-row heel - the kind which, if laid flat, would resemble an hourglass - which I'm not crazy about because again it'd be too fussy to add a tougher texture to the heel. However, I'm drawn to toe-up socks by the promise that they can be made without ribbing on the cuff. I plan to use a picot bind-off, which sadly means that this pair can't go to one of the boys, as the delicate edging would be scorned as being too feminine. But - no ribbing! I've been seduced by the siren call of no ribbing.

In case you were wondering, I knit socks using the magic loop technique, using one long circular needle. That way, I don't have to use stitch markers, as the top and bottom halves of the sock are always separated.

... cuff-down, heel flap knit back and forth, short-row cup, with stitches picked up along the flap and cup for the gusset. Sometimes I would knit a small intarsia design on the heel flap, but more often I would use a reinforcing heel stitch like eye of partridge. This is the method I used to make the socks in my last post.

I once tried what some designers refer to as the eastern method, which is knit cuff-down, with waste yarn used where the heel would be. When you get to where you would normally start the heel flap, you knit those stitches using waste yarn, slip them back to the left-hand needle, and knit them again using the good yarn. Then you do the foot and toe, which are finished in the normal way. The waste yarn is snipped out and the heel is knitted with the live stitches in the same manner as the toe.

I'm not fond of this method of construction, as leaving the heel for last means that you can't try on the sock as you go along. Also, it means using two pieces of yarn per sock instead of one continuous piece, and that means more ends to weave in.
For a while I used the Strong heel, which is named after the designer, Gerdine Crawford-Strong. It was described in the Fall 2003 Knitter's Magazine. You knit the sock cuff-down, and when you get to the heel, you increase the stitches to make the gusset. In the diagram below, the pink outline shows the area that a dutch heel flap would cover. The green dots on the leg show the increases that make the gusset.

The bottom cup of the heel is short-rowed, and the foot and toe are completed as usual.
Perhaps you can see the Strong heel in these slippers.

I eventually abandoned the Strong heel because it proved too fussy to reinforce the heel using a textured pattern.
Today, I started a pair of toe-up socks. To simplify things, which for me equals minimizing seams, instead of a provisional cast-on, I started with a regular cast-on but did double-knitting (the same method used for starting the head of my One-Seam Bear).
A toe-up sock means I have to do a short-row heel - the kind which, if laid flat, would resemble an hourglass - which I'm not crazy about because again it'd be too fussy to add a tougher texture to the heel. However, I'm drawn to toe-up socks by the promise that they can be made without ribbing on the cuff. I plan to use a picot bind-off, which sadly means that this pair can't go to one of the boys, as the delicate edging would be scorned as being too feminine. But - no ribbing! I've been seduced by the siren call of no ribbing.

In case you were wondering, I knit socks using the magic loop technique, using one long circular needle. That way, I don't have to use stitch markers, as the top and bottom halves of the sock are always separated.