  The effect of weak potential and bond disorder on the density of states of
graphene is studied. By comparing the self-consistent non-crossing
approximation on the honeycomb lattice with perturbation theory on the Dirac
fermions, we conclude, that the linear density of states of pure graphene
changes to a non-universal power-law, whose exponent depends on the strength of
disorder like 1-4g/sqrt{3}t^2\pi, with g the variance of the Gaussian disorder,
t the hopping integral. This can result in a significant suppression of the
exponent of the density of states in the weak-disorder limit. We argue, that
even a non-linear density of states can result in a conductivity being
proportional to the number of charge carriers, in accordance with experimental
findings.
