Everyone's auntie made these in the 1960s, but I've reworked the pattern to make it One-Ounce Friendly.
Looks great in variegated yarns or solid colors.
Make one for your auntie today!

Size: approx. 7.5 x 7.5 in.
Needles:  U.S. Size 6  (4 mm)
Yarn:  1 oz. utility cotton - 44-46 yds (pictured, Peaches & Creme, Gumdrop)
Gauge:  approx. 16 sts x 32 rows = 4x4 in.

Stitch Guide:  
Kfb - inc1 by knitting front and back of same st (Help?  Video)
Sl 1 purlwise - makes even loop on edges (Help?  Video)
CO 3 sts.  
Begin increase:
Row 1:  Sl 1 purlwise, Kfb , K1 - 4sts.
Row 2:  Sl 1 purlwise, Kfb, K2 - 5 sts. 
Row 3:  Sl 1 purlwise, Kfb, K3 - 6sts.
Row 4:  Sl 1 purlwise, Kfb, K4 - 7sts.

Cont each row in pattern as follows:  sl 1 purlwise, Kfb, K to end, 32 more rows, until there are 39sts.

Next row:  Sl 1 purlwise, K to end. - 39sts.

Begin decrease:
Row 1 (RS):  Sl 1 purlwise, K2tog, K to end - 38sts.
Row 2:  Sl 1 purlwise, K2tog, K to end - 37sts.

Cont each row in pattern:  Sl 1 purlwise, K2tog, K to end,  34 more rows, until 3sts rem.
BO 3sts.

Fasten off.
Weave in ends.

As with other dishcloth patterns, you may need to adjust your needle size to accommodate your knitting tension and still use just one ounce of yarn.