Large pre-trained language models reach state-of-the-art results on many different NLP tasks when fine-tuned individually; They also come with a significant memory and computational requirements, calling for methods to reduce model sizes (green AI). We propose a two-stage model-compression method to reduce a model's inference time cost. We first decompose the matrices in the model into smaller matrices and then perform feature distillation on the internal representation to recover from the decomposition. This approach has the benefit of reducing the number of parameters while preserving much of the information within the model. We experimented on BERT-base model with the GLUE benchmark dataset and show that we can reduce the number of parameters by a factor of 0.4x, and increase inference speed by a factor of 1.45x, while maintaining a minimal loss in metric performance.