We propose a new bit-interleaved coded modulation (BICM)-based cooperative communication system where different BICM modules can be optimized jointly considering the average signal to noise ratios of the direct and the two-hop Rayleigh fading channels. As such, the full benefit of BICM can be exploited in the context of cooperative communication. Our design considers cooperative communication systems with so called max-min relay selection scheme that has no loss in performance in terms of diversity- multiplexing trade off in orthogonal cooperation. The presented numerical results for rate 1/2 convolutional code with 8-ary pulse amplitude modulation equivalently 64-ary quadrature amplitude modulation show that the proposed design can offer gains up to 1.4 dB over the traditional BICM design for a target bit error rate of 10^(-6). Moreover the results show that the amount of gain depends on the relays' positions and increases with the number of relays available for selection.