The paper considers two different antenna selection schemes for space-time coded systems over flat fading channels. First we explore antenna selection at the transmitter side based on the received signal to noise ratios. We then study the joint selection of receive and transmit antennas. Both schemes assume a slowly fading channel (i.e., quasi-static fading) and require some limited feedback from the receiver to the transmitter. By computing upper bounds on the pairwise error probabilities and conducting extensive simulations, we show that the space-time coded systems achieve full diversity even with antenna selection provided that the code is full rank. These results ate extensions of earlier work on antenna selection for MIMO systems  which only considers receive antenna selection.