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We consider a cooperative transmission scheme in which the collaborating nodes may have multiple antennas. We present the performance analysis and design of space-time codes that are capable of achieving the full diversity provided by user cooperation. Our codes use the principle of overlays in time and space, and ensure that cooperation takes place as often as possible. We show how cooperation among nodes with different numbers of antennas can be accomplished, and how the quality of the interuser link affects the cooperative performance. We illustrate that space-time cooperation can greatly reduce the error rates of all the nodes involved, even for poor interuser channel quality.