An image compression apparatus and method, and a carrier wave encoded with a computer readable control program having instructions for use by a computer, perform an image compression process. A compression level is determined for use in compressing a picture image to a predetermined target data amount by iteratively compressing a reduced version of the picture image in order to determine the compression level that is to be used to compress the picture image. First, a reduced-size picture image is created from the picture image that is to be compressed. A preliminary compression target data amount is then derived, for example, based on the target data amount, the data amount of the picture image and the data amount of the reduced-size picture image. The reduced-size picture image is then compressed using a compression level. The size of the resulting compressed reduced-size picture image is compared to the preliminary compression target data amount. The compression level is then adjusted (raised or lowered) and compression of the reduced-size picture image is repeated until the resulting compressed reduced-size picture image satisfies the preliminary compression target data amount. The compression level that ultimately is derived, is then used to compress the picture image. The resulting compressed picture image will then satisfy the predetermined target data amount.