Let (L, [p]) be a finite dimensional restricted Lie algebra over an al
gebraically closed field F of characteristic p greater than or equal t
o 3, and chi is an element of L be a linear form. In this article we
investigate the structure and representation theory of those blocks of
the reduced enveloping algebra u(L, chi) that are associated to irred
ucible modules of the form u(L, chi) x (u(k, x/k)) F-lambda.