The COVID-19 pandemic has focused considerable attention on crisis standards of care (CSCs). Most public CSCs at present are effective tools for allocating scarce but not uncommon resources (like ventilators and dialysis machines). However, a different set of challenges arise with regard to extremely scarce resources (ESRs), where the number of patients in need may exceed the availability of the intervention by magnitudes of hundreds or thousands. Using the allocation of extracorporeal membrane oxygenation machines as a case study, this paper (...) argues for a different set of CSCs specifically for ESRs and explores four principles (transparency, uniformity, equity and impact) that should shape such guidelines. (shrink)