For mobile video codecs, the huge energy dissipation for external memory traffic is a critical challenge under the battery power constraint. Lossy embedded compression (EC), as a solution to this challenge, is considered in this paper. While previous studies in EC mostly focused on compression algorithms at the block level, this work, to the best of our knowledge, is the first one that addresses the allocation of video quality and memory traffic at the frame level. For lossy EC, a main difficulty of its application lies in the error propagation from quality degradation of reference frames. Instinctively, it is preferred to perform more lossy EC in non-reference frames to minimize the quality loss. The analysis and experiments in this paper, however, will show lossy EC should actually be distributed to more frames. Correspondingly, for hierarchical-B GOPs, we developed an efficient allocation that outperforms the non-reference-only allocation by up to 4.5 dB in PSNR. In comparison, the proposed allocation also delivers more consistent quality between frames by having lower PSNR fluctuation.