Model compression has gained significant popularity as a means to alleviate the computational and memory demands of machine learning models. Each compression technique leverages unique features to reduce the size of neural networks. Although intuitively combining different techniques may enhance compression effectiveness, we find that the order in which they are combined significantly influences performance. To identify the optimal sequence for compressing neural networks, we propose the Order of Compression, a systematic and optimal sequence to apply multiple compression techniques in the most effective order. We start by building the foundations of the orders between any two compression approaches and then demonstrate inserting additional compression between any two compressions will not break the order of the two compression approaches. Based on the foundations, an optimal order is obtained with topological sorting. Validated on image-based regression and classification networks across different datasets, our proposed Order of Compression significantly reduces computational costs by up to 859 times on ResNet34, with negligible accuracy loss (-0.09% for CIFAR10) compared to the baseline model. We believe our simple yet effective exploration of the order of compression will shed light on the practice of model compression.