We have generalised the standard lattice Coherent-Potential-Approximation (
CPA)/Effective-Medium-Approximation (EMA) scheme to include the case of ene
rgy dependent hopping. This case is complicated by the fact that, due to th
e detailed-balance condition, the hopping rates w(ij) are non-symmetric, i.
e. w(ij) not equal w(ji). Results for the frequency dependent diffusion coe
fficient are compared with Monte-Carlo simulations for a uniform and bimoda
l site energy distribution.