Variations of Simple Closed-coiling Stitches

Whip stitch around the coil being added, and insert the needle through the bundle of needles below it midway between the stitches in that last round. Be careful not to pierce the stitch from a previous coil. The stitches should appear separate, often as if placed on top of one another, on the basket wall.
A stitch where the needle is inserted diagonally through the top of the stitch just below it in the previous coil. The stitches spiral up the basket wall and appear interlocked resembling a chain.
Sew around the coil being added and through the center of the stitch in the previous round. This creates a split or bifurcate design where the needle and string goes through the stitch below it in the previous coil.
After producing a single simple stitch, sew through the same spot a second time, creating v-shaped forms. V-Stitches can be continued for additional coils by passing the needle through middle of a previous round of V-stitches.
Split stitches can also be used in combination with V-stitches, the slant of the spiraling pattern depending upon whether the left or right side of a 'V' is split.

Basket images adapted from Johnson: 1989
Coil Basket Forms Sheathes that hold pine needles in bunches