This paper presents a new hybrid technique for efficient compression of stereopairs . The proposed technique encompasses three processing stages: a phase difference disparity interpreter, a neural network based image compressor / decompressor, and a stereopair reconstructor. The main advantage of the proposed technique lies in a threefold data compression. The first data compression stage is realized by using the Fast Fourier Transform (FFT) for computation of the disparity. Data compression is achieved by sending both the disparity and the compressed right image. The second data compression stage is achieved by clamping the significant part of the FFT coefficients of the right image to the input layer of the neural network for further data compression. This has the advantage of reducing the number of neurons in the input layer of the neural compressor. The third data compression stage is encompassed in the data compression of the previously FFT - compressed right image through the neural net data compressor. At the receiver, the disparity, the displaced subimage and the compressed right image are used to reconstruct the left image: Experiments are performed on both random and real stereopairs. The compression ratio of the neural network depends on the number of neurons in the hidden layer. The FFT of the input parterns is used to increase the compression ratio and to speed up the learning of the neural network. Correspondence analysis is performed using the spin model to obtain the disparity map of the stereopair. System design parameters affecting the performance of the correspondence analyzer are studied to achieve optimal stereopais interpretation. This process makes it possible to transmit only the displaced regions in the left image. Another data compression step is achieved through the contour of the disparity map.