The assumption of no channel knowledge at the transmitter is inherent in the design of classical space-time codes for wireless communication. This work, on the other hand, assumes that non-perfect quantized channel information obtained from a feedback link is available at the transmitter and investigates how such channel knowledge can be incorporated into the design of space-time block codes. Efficient codes are found by means of a gradient search over a continuous alphabet. Simulation results for a Rayleigh fading scenario a system using two transmit antennas and one receive antenna show that significant gains are possible.