Within the field of signal processing, a commonly occurring problem is that of denoising signals. This problem is especially relevant within the domain of speech processing. In recent years, deep learning models have shown state of the art performance in speech enhancement applications, surpassing previous methods in both objective and subjective performance. Deep learning models have previously suffered from reduced performance on unknown noise levels, however, a recent discovery within the field of image processing, indicates that bias-free models can generalise better across noise levels. This report does not seek to create a new state of the art within speech enhancement, but instead investigates the implications of these bias-free models. For this, four different types of convolutional neural networks were selected and evaluated for their performance under both bias-free and conventional configurations. Generally, bias-free networks are not found to have any significant improvement in generalisation over regular networks. However, UNet achieved significantly better performance, in a bias-free configuration, within known SNR ranges and marginally better outside known SNR ranges. A denoising CNN with a conventional configuration performed best overall.