We study a class of composite digital filters, each has a dominating FIR component of order N and an extremely simple IIR component of order r with r-C N that are connected in parallel. We show that a constrained optimization setting known as convex-concave procedure (CCP) is naturally suited for the design of stable composite filters where the FIR and IIR components are jointly optimized in frequency-weighted minimax sense. A design algorithm based on successive CCP is presented and numerical examples are included to demonstrate that even with r =2 composite filters offer substantial performance improvement relative to their FIR-alone counterparts.