The prevalence and success of Deep Neural Network (DNN) applications in recent years have motivated research on DNN compression, such as pruning and quantization. These techniques accelerate model inference, reduce power consumption, and reduce the size and complexity of the hardware necessary to run DNNs, all with little to no loss in accuracy. However, since DNNs are vulnerable to adversarial inputs, it is important to consider the relationship between compression and adversarial robustness. In this work, we investigate the adversarial robustness of models produced by several irregular pruning schemes and by 8-bit quantization. Additionally, while conventional pruning removes the least important parameters in a DNN, we investigate the effect of an unconventional pruning method: removing the most important model parameters based on the gradient on adversarial inputs. We call this method Greedy Adversarial Pruning (GAP) and we find that this pruning method results in models that are resistant to transfer attacks from their uncompressed counterparts.