We propose two synthetic aperture radar (SAR) complex image compression schemes based on DLWT_IQ and DLWT_FFT. DLWT_IQ encodes the real parts and imaginary parts of the images using directional lifting wavelet transform (DLWT) and bit plane encoder (BPE), while DLWT_FFT encodes the real images converted by fast Fourier transform (FFT). Compared with discrete wavelet transform-IQ (DWT_IQ), DLWT_IQ improves the peak signal-to-noise ratio (PSNR) up to 1.28 dB and reduces the mean phase error (MPE) up to 21.74%; and compared with DWT_FFT, DLWT_FFT improves the PSNR up to 1.22 dB and reduces the MPE up to 20.32%. Moreover, the proposed schemes increase the PSNR up to 3.34 dB and decrease the MPE up to 50.43% as compared with the set partitioning in hierarchical trees (SPIHT) algorithm. In addition to this, we observe a novel phenomenon, that is, DLWT with direction prediction achieves a higher clustering capability for complex SAR images than DWT. Then, coding algorithm based on DLWT requires fewer coding bits than DWT for the same number of coding coefficients, and DLWT outperforms DWT in terms of rate-distortion performance even if the K-term nonlinear approximation of DWT is better than that of DLWT.