Discrimination on the basis of protected characteristics - such as race or gender - within Machine Learning (ML) is an insufficiently addressed yet pertinent issue. This line of investigation is particularly lacking within clinical decision-making, for which the consequences can be life-altering. Certain real-world clinical ML decision tools are known to demonstrate significant levels of discrimination. There is currently indication that fairness can be improved during algorithmic processing, but this has not been widely examined for the clinical setting. This paper therefore explores the extent to which novel algorithmic processing techniques may be able to mitigate discrimination against protected groups in clinical resource-allocation ML decision-support algorithms. Specifically, three state-of-the-art discrimination mitigation techniques are compared, one for each stage of algorithmic processing, when applied to a real-world clinical ML decision algorithm which is known to discriminate with regards to racial characteristics. The results are promising, revealing that such techniques could significantly improve the fairness of clinical resource-allocation ML decision tools, particularly during pre- and post- processing. Discrimination is shown to be reduced to arbitrary levels at little to no cost to accuracy. Similar studies are needed to consolidate these results. Other future recommendations include working towards a generalisable framework for ML fairness in healthcare.