This was written by Shadows guitarist Bruce Welch and Peter Chester, an old friend who had been with Welch and Hank Marvin in a band called The Five Chesternuts. Welch was looking for material and when Chester showed him the beginnings of Please Don’t Tease they finished it together.
Cliff and the Shadows recorded it on March 25, 1960. It was put to a panel of teenagers with other unreleased songs and was voted the favourite. It was released on June 24, 1960, and went to No 1.
Here is a live performance from July 1960, before which Cliff refers to the panel vote. Look at the wonderful suede shoes.