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A two-user coordinate interleaved coded cooperation scheme is proposed for quasi-static Rayleigh fading channels, where cooperative and modulation diversity techniques are properly combined to take their full advantage. Two selective cooperation schemes are considered related to whether users know the cooperation case or not. Pairwise error probability (PEP) analysis is performed for all cooperation cases and code design criteria are derived from the PEP upper bounds. Bandwidth-efficient 4-, 8- and 16-state rate 2/4 cooperative quadrature phase shift keying (QPSK) trellis codes are obtained based on these criteria by means of exhaustive computer search. The error performances of the new codes evaluated by computer simulations show their superiority compared to the corresponding best space-time codes used in cooperation with coordinate interleaving. The simulation results are supported by an upper bound on the bit error probability developed using union bounding technique.