This work proposes a redesign method for nonlinear observers to reduce the effect of a particular class of output disturbances. Specifically, it is considered a disturbance composed by a term generated from a known system and an unstructured term. The proposed approach does not require modifying the original observer and is based on adding a simple filter that includes an internal model of the disturbance generator. Sufficient conditions for stability of the proposed filter-observer architecture are given. Moreover, the approach is validated through numerical simulations.