The Consultative Committee for Space Data Systems (CCSDS) 122.0 recommendation defines a particular image data compression algorithm for space. It is based on a discrete wavelet transform (DWT) algorithm followed by bit-plane encoder stage (BPE) based on Rice codes. The low complexity and memory efficiency of the algorithm makes it suitable for use onboard a spacecraft. On the other hand, fully adaptive prediction error coder (FAPEC) is a quick entropy coder aimed to achieve excellent compression ratios under almost any situation, including large fractions of outliers in the data and large sample sizes. A new image compression solution based on the DWT stage of the CCSDS 122.0 recommendation is presented, followed by our FAPEC entropy coder, thus removing the BPE stage. The purpose is to obtain a low-complexity algorithm for image compression able to provide similar or even better compression ratios than those obtained using the CCSDS 122.0 recommendation. A prototype of DWTFAPEC, the combination of the DWT stage with FAPEC, is presented here. Its lossless operation, as well as the results with a first lossy option with selectable quality using a wide variety of images, including the official CCSDS 122.0 image corpus as well as several astronomical and ground images, is tested. The results are satisfactory, achieving significantly better compression times. The lossless ratios are very close to those of the standard, while the lossy ratios are higher (for the same level of quality loss). Thus, DWTFAPEC can be used as an alternative to CCSDS 122.0 standard for space missions.