This paper presents the design of a compensator for a novel multi-stage CIC-based decimation structure with a decreased complexity and an improved aliasing rejection recently proposed in the literature. The compensator works at a low rate, i.e., after the decimation. As a result, the complexity introduced by the compensator is low. The overall complexity of the compensated filter is expressed in the number of adders per output sample (APOS). The magnitude characteristic of the compensator is presented as a product of two sinusoidal functions. The magnitudes of the sinusoidal functions are obtained using particle swarm optimization (PSO), resulting in a low maximum passband deviation in the passband of interest. We consider here the wideband compensation. The resulting compensated multi-stage decimation filter has a low passband deviation in the wide passband, an improved aliasing rejection, and a low number of APOS. The proposed compensated filter is compared with similar filters from the literature.