Given the multitude of newly available genetic tests in the face of limited healthcare budgets, the European Society of Human Genetics assessed how genetic services can be prioritized fairly. Using (health) benefit maximizing frameworks for this purpose has been criticized on the grounds that rather than maximization, fairness requires meeting claims (e.g. based on medical need) equitably. This study develops a prioritization score for genetic tests to facilitate equitable allocation based on need-based claims. It includes attributes representing health need associated with hereditary conditions (severity and progression), a genetic service's suitability to alleviate need (evidence of benefit and likelihood of positive result) and costs to meet the needs. A case study for measuring the attributes is provided and a suggestion is made how need-based claims can be quantified in a priority function. Attribute weights can be informed by data from discrete-choice experiments. Further work is needed to measure the attributes across the multitude of genetic tests and to determine appropriate weights. The priority score is most likely to be considered acceptable if developed within a decision process which meets criteria of procedural fairness and if the priority score is interpreted as "strength of recommendation" rather than a fixed cut-off value.