Let k be an algebraically closed field of characteristic p > 0, and let G be a connected, reductive algebraic group over k. In [8] and [11], conditions on the dimension of rational G modules were seen to imply semisimplicity of these modules. In [8], certain of these conditions were extended to cover the finite groups of Lie type. In this paper, we extend some of the results of [11] to cover these finite Lie type groups. The main such extension is the following result.