COVAX, the global initiative on COVID-19 vaccines, has set the target of achieving a COVID-19 vaccination coverage of up to 30% of the population of 135 countries in 2 years. Here, we argue that COVAX should anticipate important and unforeseen challenges with regard to sanctioned countries. For those, COVAX needs to provide a higher percentage of the vaccines. Otherwise, the problems of vaccination will linger, risking the advent of new variants and preventing an effective global response in reigning the pandemic under control.