We consider a diffusion perturbed classical compound Poisson risk modelin the presence of a constant dividend barrier. Integro-differential equationswith certain boundary conditions for the expected discounted penalty(Gerber-Shiu) functions (caused by oscillations or by a claim) are derivedand solved. Their solutions can be expressed in terms of the Gerber-Shiufunctions in the corresponding perturbed risk model without a barrier. Finally,explicit results are given when the claim sizes are rationally distributed.