Compositional fluctuations in the strands of a nematic network lead to variations in intrinsic anisotropy. We show that these fluctuations can have a large effect if the chains are persistent. We calculate the threshold to the semisoft striped state. This can be large (and the semisoft moduli large) even if the chain anisotropies are small. Softness is violated if the fluctuating chains are cross-linked in the nematic state. A case where smectogenic elements are incorporated into the network is given. The Landau free energy is derived and shown to have linear terms of semisoft systems. The nonstriped nematic elastomer instability experiments are re-examined in the light of our theoretical results.