An ethical framework for pandemic healthcare distribution typically encompasses multiple ethical values. However, integrating various ethical values and distributive principles into a single framework raises concerns about their compatibility and the overall coherence of the framework. This issue of value compatibility could lead to moral inconsistencies within the ethical framework, leading to practical indetermination when facing conflicting implications. This paper offers a methodological resolution to the compatibility problem, serving as an effective tool to mitigate the impact of value conflicts where (...) possible. It proposes four pathways: specifying values rather than balancing them, incorporating values rather than weighing them, reinforcing values rather than aggregating them, and seeking scientific evidence. By developing coherent ethical frameworks where values do not contradict each other, this approach also enhances practical ethical decision-making. Using the COVID-19 vaccine distribution as a case study, this approach demonstrates how conflicting values can yield practical prioritization strategies, such as allocating vaccines to healthcare and essential workers, addressing multiple layers of disadvantage, and assessing age-related prioritization. Reflecting on the compatibility of values within ethical frameworks offers crucial insights beyond COVID-19, contributing to the development of robust ethical frameworks for future public health crises. (shrink)