This paper introduces the design of context-based models of contours in the wavelet domain, which are used to construct generalized lifting (GL) mappings for image compression. The GL context-based mapping may significantly reduce the signal energy and the resulting bitrate. Here, we propose a strategy to define a reduced set of structured models to design the GL. The models capture the contour structures and are contrast-invariant. Initial experimental results applying the strategy on a wavelet subband exhibit potential gains. Iterations of the GL scheme as well as an adaptive entropy coding strategy may increase the coding gain.