In neural network compression, most current methods reduce unnecessary parameters by measuring importance and redundancy. To augment already highly optimized existing solutions, we propose linearity-based compression as a novel way to reduce weights in a neural network. It is based on the intuition that with ReLU-like activation functions, neurons that are almost always activated behave linearly, allowing for merging of subsequent layers. We introduce the theory underlying this compression and evaluate our approach experimentally. Our novel method achieves a lossless compression down to 1/4 of the original model size in over the majority of tested models. Applying our method on already importance-based pruned models shows very little interference between different types of compression, demonstrating the option of successful combination of techniques. Overall, our work lays the foundation for a new type of compression method that enables smaller and ultimately more efficient neural network models.