We propose a simple method to construct good space-time trellis codes. As with any trellis code, space-time trellis codes can be realized with a convolutional encoder followed by a mapping rule. Herein we devise improved space-time trellis codes by optimizing the convolutional code and mapper for the Jakes time correlated flat fading model. This new, simple method can be used to construct both nonrecursive and recursive space-time codes where the latter is essential for serial concatenation. A simple encoding system is presented which is 1.8 dI3 away from channel capacity for the 2-inputI2-output fully interleaved MIMO channel.