A continued fraction technique is used to derive an approximation to the density of states of a disordered alloy with a tree of Bethe lattice. The approximation in the case of only diagonal disorder provides a new simple derivation of the coherent potential approximation for a certain density of states. For an alloy with both diagonal and off-diagonal disorder the density of states is given in terms of the solution of a certain cubic equation. The self energy in this case is also obtained and used to provide the starting point for a theory of alloys with both diagonal and off-diagonal disorder and a general lattice which is equivalent to a special case of the theory of Blackman et al. Extensive calculations are presented.