The purity theorem (A. J. de Jong and FO, 2000) says that if a Newton polygon jumps in a family, then it jumps already in codimension one. I will present a new proof of this theorem, based on ideas by Vasiu. Also I will comment on "purity" for finite group schemes, and state a conjecture for truncated Barsotti-Tate groups. Reference: A. J. de Jong and F. Oort, Purity of the stratification by Newton polygons. Journ. A.M.S. vol. 13, 2000, 209 - 241.