For a connected orientable hyperbolic surface S without boundary and of finite topological type, the Johnson kernel \(\mathcal {K}(S)\) is the subgroup of the mapping class group of S generated by Dehn twists about separating simple closed curves on S. We prove that \(\mathcal {K}(S)\) is generated by the Dehn twists about separating simple closed curves on S bounding either: a closed subsurface of genus 1 or 2; a closed subsurface of genus 1 minus one point; a closed disc minus two points.
