The paper proposes a general framework for the importance coding of still images to maximise the interpretability versus bitrate performance. The interpretability of an image to achieve maximum content recognition is important in a diverse range of applications such as surveillance and medical. Importance coding aims to address this problem by prioritisation of the encoded image bit-stream based on the importance of regions in an image. Consequently, the most important features required for interpretability are encoded and transmitted earlier in the encoded image bit-stream. The notion of importance maps, which provide a systematic approach for the assignment of relative importance of regions in an image, are presented and its use in importance coding is developed. One highly desirable advantage of the proposed importance coding framework is that it can be implemented by the EBCOT (embedded block coding with optimised truncation) coder, which has been selected as the core-coding algorithm in JPEG 2000.