Popular multiplierless decimation filter is the cascaded-integrator-comb (CIC) filter. However, the magnitude response of this filter has a high passband droop and poor selectivity. One technique for improving the response is sharpening. In the design of sharpened CIC filters, the Kaiser-Hamming method is well established. It results in maximally flat filters. Recently, the weighted least-squares method has been proposed. It improves the response better than the Kaiser-Hamming method. In this paper, we present a method for the design of sharpened CIC filters by using the weighted minimax error criterion. The method is based on the iterative reweighted least-squares procedure. The features of the presented method are illustrated with the design of narrowband and wideband filters. It is shown that the proposed filters are preferable compared to the maximally flat and the weighted least-squares counterparts.