Disclosed is a method of compressing information for storage in a fixed size memory. The data items (D(k)) that constitute the information are divided into pieces (D(s,k)) of decreasing significance. For example, the DCT blocks of an image are hierarchically quantized (3). The memory (5) is organized in corresponding memory layers (501-504). Successive memory layers have a decreasing number of memory locations. Every time a data item is applied to the memory, its less significant data pieces will have to compete with corresponding data pieces of previously stored data items. Depending on its contribution to perceptual image quality, the applied data piece is stored or the stored data piece is kept. Links (511-513, 521-522) are stored in the memory to identify the path along which a data item is stored. Eventually, the image is automatically compressed so as to exactly fit in the memory. FIG. 2.