Yes, “Preemie Shower Cap” is a terrible name. This was designed for the Knitmore Girls’ Head to Toe contest, which asked for hats sized for premature babies that could be made with leftover sock yarn--winning submissions are here.

The yarn used for this hat was Red Heart Heart & Sole in Watercolor Stripe, but any yarn can be used; in fact, I think this hat could be made to any size by following the same proportions: knit the I-cord brim to fit, increase the stitches by 1/3 (k2, YO) to make the body of the hat, knit until the body of the hat is 2/3 as long as you want it, then decrease as in the pattern to 6 stitches and close off the top of the hat. Use needles appropriate to your yarn.