Stranded Ladderback Jacquard is a fancy, intimidating name for a super simple, super fast technique that will improve your stranded colourwork.
It eliminates the need to twist stitches to avoid long floats, it eliminates colour blips on the right side, and it leaves the fabric almost as stretchy as non-colourwork knitting.
Cast on the number of stitches called for in your pattern. Work any ribbing (hat brim, sock cuff, etc.)
Work the two setup rounds before beginning colourwork.
Setup Round One: *k3, k1fb, repeat from *
Setup Round Two: *k4 with MC, p1tbl with CC, repeat from *
MC = Main Colour
CC = Contrast Colour
k1fb = knit into the front of the stitch, leave it on the needle, knit into the back of the stitch, slide stitch to right needle
p1tbl = purl into the back of the stitch (this will mount the stitch opposite of how it is normally oriented on the needle.)
Working the Stitch:
Knit 4 stitches in your colourwork sequence
Bring both yarns to the front, and purl using only the contrast colour.
Bring both yarns to the back, and continue to knit in your pattern, pausing every 4 stitches to bring both yarns to the front and purl with the contrast colour.
Returning to Main Colour:
When you reach a purl stitch, work it as a k2tog with the stitch to the left. This will drop the purl column to the back, hiding it completely, and you can continue in a solid colour.