Newborn Modern Cloth Nappies – Tiny Nappies – Premmie Nappy – Newborn Cloth Nappies are available in small and extra small sizes. – OSFM (one-size-fits-most) nappies will be bulky on a tiny newborn. Some newborn nappies tie on. – Other small nappies have a scoop at the front for the umbilical cord. – Your baby is eco-friendly right from the start.