On sheets of conjugacy classes in good characteristic

We show that the sheets for a connected reductive algebraic group $G$ over an algebraically closed field in good characteristic acting on itself by conjugation are in bijection with $G$-orbits of triples $(M, Z(M)^\circ t, O)$ where $M$ is the connected centralizer of a semisimple element in $G$, $Z(M)^\circ t$ is a suitable coset in $Z(M)/Z(M)^\circ$ and $O$ is a rigid unipotent conjugacy class in $M$; or, equivalently they are in bijection with $G$-orbits of pairs $(L,\,O)$ with $L$ a Levi factor of a parabolic subgroup of $G$ and $O$ a rigid conjugacy class of $[L,\,L]$. Any semisimple element is contained in a unique sheet $S$ and $S$ corresponds to a triple with $O=\{1\}$. The sheets in $G$ containing a unipotent conjugacy class are precisely those corresponding to triples for which $M$ is a Levi factor of a parabolic subgroup of $G$ and the class is unique.