This paper presents efficient modification of the CICcosine decimation filter. The second order compensator filter is introduced at low rate in order to improve the passband of interest of the overall filter. The coefficients of the compensator filter are presented in a canonical signed digits (CSD) form, and can be implemented using only adders and shifts. Consequently, the resulting filter is a multiplierfree filter and exhibits a high attenuation in the stopband, as well as a low passband droop.