Image compression using neural networks have reached or exceeded non-neural methods (such as JPEG, WebP, BPG). While these networks are state of the art in ratedistortion performance, computational feasibility of these models remains a challenge. We apply automatic network optimization techniques to reduce the computational complexity of a popular architecture used in neural image compression, analyze the decoder complexity in execution runtime and explore the trade-offs between two distortion metrics, rate-distortion performance and run-time performance to design and research more computationally efficient neural image compression. We find that our method decreases the decoder run-time requirements by over 50% for a stateof-the-art neural architecture.