Learned image compression has gradually surpassed traditional image compression methods in terms of performance. However, in practical deployment, it frequently encounters challenges related to computational complexity and the rigidity of large models. Existing dynamic image compression models can only adjust model bit rate and complexity at a coarse granularity, and their entropy models lack adjustability. To address these issues, this paper constructs a fine-grained adjustable entropy model (FAEM), and proposes a complementary complexity-rate-distortion joint optimization algorithm. This approach allows a single network to seamlessly transition among 13 sub-models with varying widths, enabling precise control over model bit rate, computational complexity, and hardware inference time.