In a traditional direct detection (DD) optical communication system, performance loss is inevitably caused by the interaction between dispersion and square-law detection of a photodetector. Based on a DD optical communication system using Stokes space multiplexing, a spectrum compression algorithm is proposed to optimize the phase of a transmitted signal sequence, which transforms a three-dimensional Stokes space signal to a four-dimensional Jones spatial signal with 3/4 bandwidth, thus enabling the dispersion pre-compensation without performance loss and extra hardware cost. Since this ideal spectrum compression requires global optimization algorithm with high complexity, we propose a simplified look-up-table based phase optimization algorithm. Simulation results show that when the optimization length is 7 symbols, the difference between the peak and the valley of the spectrum is about 17 dB, which effectively decreases the bandwidth requirement of the transmitter.