  In this article we consider the centre of the reduced enveloping algebra of
the Lie algebra of a reductive algebraic group in very good characteristic p >
2. The Harish-Chandra centre maps to the centre of each reduced enveloping
algebra and, using a combination of induction and deformation arguments, we
describe precisely for which p-characters this map is surjective: it is if and
only if the chosen character is regular. This provides the converse to a
theorem of Mirkovi\'{c} and Rumynin.
