The integer wavelet transform (IWT), applied to lossy-image compression, yields rate-distortion performance which is generally, slightly inferior to the discrete wavelet transform (DWT). In this paper, we propose a simple method which, based on the analysis of the IWT signal representation mechanism, is able to raise the IWT performance up to the DWT level. The method can be profitably employed for the implementation of a truly common-core lossless and lossy compression algorithm, with negligible loss of performance with respect to the classical, real-valued transform.