For a restricted Lie
superalgebra g over an algebraically closed field of characteristic p > 2, we generalize
the deformation method of Premet and Skryabin to obtain results on the p-power
and 2-power divisibility of dimensions of g-modules. In particular, we give a new
proof of the super Kac–Weisfeiler conjecture for basic classical Lie superalgebras. The
new proof allows us to improve optimally the assumption on p. We also establish a
semisimplicity criterion for the reduced enveloping superalgebras associated with
semisimple p-characters for all basic classical Lie superalgebras using the technique of
odd reflections.