The special baby unit at the nearest hospital uses mitts and sleeves to stop the premature babies interfering with the equipment needed to look after them. (They do not require bootees or ordinary baby mitts; if you plan to knit for your local hospital it is worth checking what they require.)
I was lent a mitt and a sleeve to copy. I worked out my own patterns using double knitting baby yarn. Only knit (k) and purl (p) stitches are required.
Using 3.5mm needles cast on 32 stitches. Work 14 rows in k.1. p.1 rib.
Change to 4mm needles and work 26 rows in stocking stitch.
Shape top: Next row K.1, k. 2 together, k. 14, k. 2 tog., k. to end.
Next row P.12, p.2 tog., p.13, p.2 tog., p.1.
Next row K.1, k 2. tog., k. 12, k.2 tog.,k. to end.
Next row P.11, p. 2 tog., p. 10, p.2 tog., p.1.
Cast off. Join seam neatly.
Using 5mm needles cast on 26 stitches.
Work K2. P2. rib until sleeve measures 5ins.
Join sides neatly.