(These also fit peanut butter jars nicely.)
All abbreviations are standard.
Variation 1 uses hemp twine on size 5 (US) needles and includes a strap that buttons onto a 1/2" or 3/4" button.
Variation 2 is exactly the same as 1, except knit with DK weight wool yarn (I expect fingering or sock yarn would also work and have a lacier appearance) on size 9 (US) needles and omitting the strap.
Variation 3 is the simplest and is knit with worsted weight wool yarn on size 7 (US) needles. This variation leaves out the decorative pattern with straight knitting from round 12 up to the decrease round where the jar slightly narrows at the top (quick, easy to knit, and uses up odd scraps of yarn perfectly).
round 1: *k1, kfb*, repeat from * to * 3 more times (12 st)
round 2 (and all even rounds): knit
round 3: *k2, kfb*, repeat 3 times (16 st)
round 5: *k3, kfb*, repeat 3 times (20 st)
round 7: *k4, kfb*, repeat 3 times (24 st)
round 9: *k5, kfb*, repeat 3 times (28 st)
round 11: purl
round 12-14: knit
rounds 15-20: follow decorative pattern below (unless following variation 3)
rounds 21+: Knit until your cozy measures 2 1/12" past the purl row (this was 9 rows of straight knitting for me with both the hemp twine and the DK weight yarn).
Repeat decorative pattern.
Knit 2 more rounds, followed by a decrease round.
decrease round: *knit 5, k2tog*, repeat 3 times
Then purl one round before binding off.
Bind off VERY loosely (this is important or you won't be able to stretch it over the bottom of the jar).
~if adding a strap (as in variation 1) only bind off 22 stitches and follow directions for strap
Weave in ends.
round 1: *k6, p1*, repeat 3 more times
round 2: p1, *yo, ssk, k2tog, yo, p3*, repeat from * to * 3 more times but ending with p2
round 3: p2, *k2, p5*, repeat from * to * 3 times but ending with p3
round 4: *p6, k1*, repeat 3 times
round 5: *k2tog, yo, p3, yo, ssk*, repeat 3 times
round 6: k3, *p1, k6*, repeat from * to * 3 times but ending with p3
for the strap:
After binding off 22 stitches, knit to the end of the bind off row. You should have 6 stitches on your needle. Knit 5 stitches and slip the last stitch (knit-wise) with yarn in front. Repeat this until desired length and finish up with a buttonhole.
buttonhole row: k1, k2tog, yo, k2, slip last stitch with yarn in front
Knit 2 more rows with slipping the last stitch and then bind off.
Sew button onto the main body of the cozy across from the strap.