In this paper, a new lossy image compression technique based on adaptive variable degree variable segment length Chebyshev polynomials is proposed. The main advantage of this method over JPEG is that it has a direct individual error control where the maximum error in gray level difference between the original and the reconstructed images can be specified by the user. This is a requirement for medical applications where near lossless quality is needed. The compression is achieved by representing the gray level variations across any determined section of a row or column of an image by the coefficients of a Chebyshev polynomial. The performance of the method was evaluated on a number of test images and using some quantitative measures compared to the well known JPEG compression techniques.